For this case we have the following data:
Polynomial function of grade 5
Given roots: -2, 2,
Having an imaginary root given by , the other root, in the same imaginary way, must be given by its complex conjugate, that is,
.
In this way, the fourth root is given by:
Since the polynomial function is grade 5, it must have 5 roots. Thus, the fifth root must be given by a real number.
Thus, the roots of the polynomial function are given by: three real roots and two imaginary roots.
Answer:
Option D