Three roots of a fifth degree polynomial function f of x are negative 2 , 2 , and 4 plus i Which statement describes the number and nature of all roots for this function?

For a polynomial with real coefficients, nonreal complex roots occur in conjugate pairs. Since 4 + i is a root, 4 − i must also be a root. Together with the given real roots −2 and 2, that accounts for four roots; the fifth root must be real. So the function has three real roots and two nonreal (imaginary) roots, which is choice B.

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