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?

Well there are 2 imaginary roots, if you are given 4 + i the conjugate is also a root 4 - i these roots come in pairs sometimes written x=4±i you are told 2 roots are real, -2, 2 a degree 5 polynomial has 5 roots so since imaginary roots come in pairs, the 5th root has to be real... hope that helps