在线求解二次方程

甲二度方程是以下形式的等式一种X2+ b x + c = 0${\displaystyle \mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">C</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$。这种类型的方程式也称为二次方程式。为了解决这些方程， 用以下公式计算 判别 式Δ =b2− 4 a c${\displaystyle <font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\Delta </font></font><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">4</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">C</font></font>}}$。
判别式是确定方程式解的数量的数字。

• 当判别为正时，二阶方程允许两个解，分别由下式给出 - b -Δ--√2个${\displaystyle \frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\sqrt{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\Delta </font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}}}$ 和 − b +Δ--√2个${\displaystyle \frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\sqrt{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\Delta </font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}}}$;
• 当判别为零时，二次方程只接受一个解，即为双根，由公式给出  − b2个${\displaystyle \frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}}}$;
• 当判别为负时，次数为2的多项式方程不接受解。

在线求解二次方程式有一种X2+ b x + c = 0${\displaystyle \mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">C</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$很快，当变量不是模棱两可时，只需输入要求解的方程式并单击计算，即可返回结果。还显示了导致二次方程式分解的计算步骤。求解以下二次方程

X2+ 2 x - 3 = 0${\displaystyle {\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">3</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$，只需 在计算区域中输入表达式 x ^ 2 + 2x-3 = 0，然后单击“计算”即可返回结果

[ x = − 3 ; x = 1 ]${\displaystyle <font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">[</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">3</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">;</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">]</font></font>}$
为了解决下面的二次方程， X2+ x = 2X2+ 4 x + 1${\displaystyle {\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">4</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}$，只需 在计算区域中键入表达式 x ^ 2 + x = 2x ^ 2 + 4x + 1，然后单击计算，即可返回结果[ x =− 3 +5–√2; x =- 3 -5–√2]${\displaystyle <font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">[</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">3</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\sqrt{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">5</font></font>}}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">;</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">3</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\sqrt{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">5</font></font>}}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">]</font></font>}$
也可以求解形式的等式 一种X2+ b x + cG（x ）= 0${\displaystyle \frac{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">b</font></font>}\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">C</font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">G</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">（</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">）</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$ 或可能采用这种形式的方程式，g（x）表示一个函数。

二次方程求解器的一些示例

• equation_solver（1个x + 1=1个3⋅ X ）${\displaystyle <font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">（</font></font>\frac{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\frac{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">3</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">\cdot </font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">）</font></font>}$ 退货 [− 1 +13--√2;- 1 -13--√2]${\displaystyle <font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">[</font></font>\frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">+</font></font>\sqrt{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">13</font></font>}}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">;</font></font>\frac{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\sqrt{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">13</font></font>}}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">]</font></font>}$
• X2− 1x − 1= 0${\displaystyle \frac{{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">2</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">--</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">1个</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$ 返回-1，则分子的计算将整个定义考虑在内，并允许两个根1和-1，但对于x = 1，分母为零，所以1不能作为方程的解。

查看下面更多的实例题