Question

State how many imaginary and real zeros the function has.

f(x) = x4 - 15x2 - 16

4 imaginary; 0 real
3 imaginary; 1 real
2 imaginary; 2 real
0 imaginary; 4 real

Answer 1

2 imaginary; 2 real

Explanation:

You can factor it as ...

f(x) = (x^2 -16)(x^2 +1) . . . . . . . . . x^2-16 is the difference of squares

= (x -4)(x +4)(x^2 +1)

The two linear factors have real zeros; the quadratic factor has two imaginary zeros. There are 2 imaginary and 2 real zeros.