Chapter 6.7, Problem 1ACYP

To determine

Solve the given equation. State the number and type of roots.

Answer to Problem 1ACYP

The equation $x^3+2x=0$ has one imaginary root 0, and two imaginary root $\sqrt{2}i,-\sqrt{2}i$ .

Explanation of Solution

Given information:

The equation $x^3+2x=0$ .

  $x^3+2x=0$

Taking x common from LHS of equation.

  $x\left(x^2+2\right)=0$

By the above equation, we get that one of or both the term $x$ and $\left(x^2+2\right)$ are zero,

  $\begin{array}{l}{x}^2+2=0\\ \\ x^2=-2\\ \\ x=\sqrt{-2}\\ \\ \sqrt{2}i,-\sqrt{2}i\end{array}$

  $x=0$

The equation $x^3+2x=0$ has one imaginary root 0, and two imaginary root $\sqrt{2}i,-\sqrt{2}i$ .