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

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 6th degree polynomial, it can have 0, 2, 4, or 6 real zeros because complex roots occur in conjugate pairs. If there are complex roots, they reduce the number of real roots, but the total count of real and complex roots will always equal the degree of the polynomial.

Provide an Appropriate Response