# How do you find the zeros of g(x)=x^4-5x^2-36?

Nov 1, 2016

$g \left(x\right) = {x}^{4} - 5 {x}^{2} - 36$ has 4 zeros, $x = - 3 , 3 , - 2 i \mathmr{and} 2 i$

#### Explanation:

Given:

$g \left(x\right) = {x}^{4} - 5 {x}^{2} - 36$

Let $u = {x}^{2}$

$g \left(u\right) = {u}^{2} - 5 u - 36 = 0$

$0 = {u}^{2} - 5 u - 36$

$0 = \left(u - 9\right) \left(u + 4\right)$

$u = 9 \mathmr{and} u = - 4$

$x = \pm 3 \mathmr{and} x = \pm 2 i$

$g \left(x\right) = {x}^{4} - 5 {x}^{2} - 36$ has 4 zeros, $x = - 3 , 3 , - 2 i \mathmr{and} 2 i$