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) 0, 2, 4, or 6
B) 6
C) 2, 4, or 6D)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 Complex Conjugate Root Theorem, any non-real roots must come in conjugate pairs. Thus, a 6th-degree polynomial could have 0, 2, 4, or 6 real zeros, with the rest being complex conjugates if not all are real.

Provide an Appropriate Response