What are the possible numbers of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree six?
A) 1, 3, or 5
B) 0, 2, 4, or 6
C) 2, 4, or 6
D) 6

Question

Quizplus · Accepted Answer

A polynomial of degree n can have up to n real zeros (counting multiplicities), and by the Fundamental Theorem of Algebra, it must have exactly n roots (real or complex) in total. For a sixth-degree polynomial, this means it can have 0, 2, 4, or 6 real zeros, with the rest being complex conjugate pairs if not real.

What Are the Possible Numbers of Real Zeros (Counting Multiplicities)