# How do you find the complex roots of a^3+2a^2-8a=0?

Jun 28, 2017

See below.

#### Explanation:

We can see that all of the variables have an $a$, so we can factor this out immediately.

$a \left({a}^{2} + 2 a - 8\right) = 0$

So, one solution is $a = 0$. The other solutions pertain to the quadratic, which we can find using factoring.

${a}^{2} + 2 a - 8 = 0$

${a}^{2} - 2 a + 4 a - 8 = 0$

$a \left(a - 2\right) + 4 \left(a - 2\right) = 0$

$\left(a + 4\right) \left(a - 2\right) = 0$

So,

$a = 2 , - 4 , 0$, and there are no complex roots.