Question

State how many imaginary and real zeros the function has.
f(x) = x4 - 15x2 - 16

Answer 1

2 real roots

2 imaginary roots

Explanation:

So we have the function:

`f(x)=x^4-15x^2-16`

And we want to find its zeros.

First, let u equal x². So:

`0=u^2-15u-16`

Factor:

`0=(u-16)(u+1)`

Zero Product Property:

`u-16=0\text{ or }u+1=0`

Add 16; Subtract 1. Replace u:

`x^2=16\text{ or }x^2=-1`

Take the square root:

`x=\pm 4\text{ or }x=\pm i`

So, our solutions are 2 real roots and 2 imaginary roots.