Question

How do you find the zeroes of `f(x) = x^4= -7x^2 -144`?

Answer 1

I found:
`x_1=4`
`x_2=-4`
`x_3=3i`
`x_4=-3i`

Explanation:

I start supposing that the second `=` sign is not necessary, so:
`f(x)=x^4-7x^2-144`
You can find the zeroes (`x` values that makes your function equal to zero) by setting your function equal to zero and get:
`x^4-7x^2-144=0`

set `x^2=u` so you get:
`u^2-7u-144=0`
Using the Quadratic Formula you get:
`u_(1,2)=(7+-sqrt(49-4(-144)))/2=(7+-25)/2`
so you get 2 solutions:
`u_1=16`
`u_2=-9`
But `x^2=u` so `x=+-sqrt(u)`

You get 4 zeroes for your function (2 Real and 2 Immaginary):
`x_1=sqrt(16)=4`
`x_2=-sqrt(16)=-4`
`x_3=sqrt(-9)=3i`
`x_4=-sqrt(-9)=-3i`