Question

Three roots of a fifth degree polynomial function f(x) are -2, 2, and 4 + i. Which statement describes the number and nature of

Answer 1

We know that imaginary roots always come in pairs, so we already know 4 solutions

-2, 2, 4 + i and a pair of 4 + i

Since imaginary roots always come in pairs we wont have more than 2 imaginary roots, since its a fifth degree root and we can only have 5 roots

So for sure, we will have 3 real roots and 2 imaginary roots

Last option, f(x) has three real roots and two imaginary roots