# How do you find all the zeros of f(x)=2x^4-2x^2-40?

Mar 1, 2016

$x = - \sqrt{5} , \sqrt{5} , - 2 i , 2 i$

#### Explanation:

Set $f \left(x\right) = 0$.

$2 {x}^{4} - 2 {x}^{2} - 40 = 0$

Divide both sides by $2$.

${x}^{4} - {x}^{2} - 20 = 0$

We can make this resemble a quadratic if we let $u = {x}^{2}$:

${u}^{2} - u - 20 = 0$

Factor to see that:

$\left(u - 5\right) \left(u + 4\right) = 0$

So:

$u = 5 \text{ "" ""or"" "" } u = - 4$

Since $u = {x}^{2}$,

${x}^{2} = 5 \text{ "" ""or"" "" } {x}^{2} = - 4$

These give

$x = \pm \sqrt{5} \text{ "" "" "" } x = \pm 2 i$