Question

Solve x^3 - 125 =0 complex roots

Answer 1

`x=5,-(5)/(2)+\frac{5\sqrt[]{3}}{2}i,-(5)/(2)-\frac{5\sqrt[]{3}}{2}i`

Explanation:

We have the following equation:

`\begin{gathered} x^3\: -\: 125\: =0\: \\ x^3\: \: =125\: \end{gathered}`

Solving for x:

`\begin{gathered} x=\sqrt[3]{125} \\ x_1=5 \\ x_2=\sqrt[3]{125}\cdot\frac{-1+\sqrt[]{3}}{2}i=5\cdot\frac{-1+\sqrt[]{3i}}{2}=-(5)/(2)+\frac{5\sqrt[]{3}}{2}i \\ x_3=\sqrt[3]{125}\cdot\frac{-1-\sqrt[]{3}}{2}i=5\cdot\frac{-1-\sqrt[]{3i}}{2}=-(5)/(2)-\frac{5\sqrt[]{3}}{2}i \end{gathered}`