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

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 all roots for this function?

f(x) has two real roots and one imaginary root.
f(x) has three real roots.
f(x) has five real roots.
f(x) has three real roots and two imaginary roots.

Answer 1

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

The statement that describes the number and nature of all roots for this function is: f(x) has three real roots and two imaginary roots.