Provide an appropriate response.
-Let P be a polynomial function with real coefficients. If -3, 10, -3 + 8i, and 7 - 6i are zeros of P, what is the smallest possible degree that P can have?
A) 8
B) 4
C) 5
D) 6

Question

Quizplus · Accepted Answer

For polynomials with real coefficients, complex roots must occur in conjugate pairs. Thus, the zeros -3 + 8i and 7 - 6i imply that -3 - 8i and 7 + 6i are also zeros. This gives a total of 6 distinct zeros: -3, 10, -3 + 8i, -3 - 8i, 7 - 6i, and 7 + 6i. Therefore, the smallest possible degree of the polynomial is 6.

Provide an Appropriate Response