Answer:
2 real roots
2 imaginary roots
Step-by-step explanation:
So we have the function:
[tex]f(x)=x^4-15x^2-16[/tex]
And we want to find its zeros.
First, let u equal x². So:
[tex]0=u^2-15u-16[/tex]
Factor:
[tex]0=(u-16)(u+1)[/tex]
Zero Product Property:
[tex]u-16=0\text{ or }u+1=0[/tex]
Add 16; Subtract 1. Replace u:
[tex]x^2=16\text{ or }x^2=-1[/tex]
Take the square root:
[tex]x=\pm 4\text{ or }x=\pm i[/tex]
So, our solutions are 2 real roots and 2 imaginary roots.
