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?

Answer 1

Since the polynomial is of degree 5 and has three known roots, it has two unknown roots. If the coefficients of the polynomial are real, then the two unknown roots must be either real or a conjugate pair of complex numbers. If the coefficients of the polynomial are complex, then the two unknown roots can be any complex numbers. Therefore, the statement that describes the number and nature of all roots for this function depends on whether the coefficients of the polynomial are real or complex.