Question

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

Answer 1

Answer:

2 real roots

2 imaginary roots

Step-by-step 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.