求解三次方程

方程计算器可求解某些三次方程。如果方程式允许有明显的解决方案，则计算器能够找到三次多项式的根。因此，计算器将无问题地解决像这样的三次方程：（- 6 + 11 ⋅ X - 6 ⋅X2+X3= 0${\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;">6</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;">11</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>\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;">6</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>}}^{\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>}}^{\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>}}$）。

同样，三次方程的解将伴随有解释，这使得找到结果成为可能。

使用零积属性求解方程

的零产品属性是用来解决形式A * B = 0的等式，该等式是零仅当A = 0或B = 0。为了解决这种类型的方程可以如果A和B是阶多项式来进行小于或等于2。还将显示导致方程式解析的计算细节。也可以求解形式的等式一种ñ= 0${\displaystyle {\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">一种</font></font>}}^{\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">ñ</font></font>}}<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">=</font></font>\mathrm{<font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;"><font\; style="box-sizing:\; border-box;\; transition:\; none\; 0s\; ease\; 0s;\; vertical-align:\; inherit;">0</font></font>}}$，如果A是一个较低的多项式或等于2。

使用零积属性求解方程的一些示例。

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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><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;">4</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:\; 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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>}<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>}$ 退货 [ − 1 ; 4 ；− 3 ]${\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><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;">4</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>}$
• （X2− 1 ）（x + 2 ）（x − 3 ） = 0${\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>}}^{\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>}<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;">X</font></font>}<font\; style="box-sizing:\; border-box;\; transition:\; 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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>}}$ 退货 [ 1 ; − 1 ; − 2 ; 3 ]${\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;">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><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><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>}<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>}$。

查看下面更多的实例题