# How do you find all the zeros of f(x) = x^4+ -7x^2 -144?

Mar 11, 2016

$x = \pm 4 , \pm 3 i$

#### Explanation:

$f \left(x\right) - {x}^{4} - 7 {x}^{2} - 144$ (Since $\text{+ -} = -$)

Let $z = {x}^{2}$
$f \left(x\right) = {z}^{2} - 7 z - 144$

To find all zeros set $f \left(x\right) = 0$
${z}^{2} - 7 z - 144 = 0$

Factorizing:
$\left(z + 9\right) \left(z - 16\right) = 0$

Therefore $z = - 9 \mathmr{and} 16$

But $z = {x}^{2} \to x = \pm \sqrt{z}$

With $z = - 9 , x = \pm 3 i$
And with $z = 16 , x = \pm 4$