College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.6 - Complex Numbers; Quadratic Equations in the Complex Number System - 5.6 Assess Your Understanding: 44

Answer

The function has three zeros. Since $-i$ and $3+i$ are complex zeros, then their conjugates $-i$ and $3-i$ must also be zeros of the function.

Work Step by Step

RECALL: The Conjugate Pairs Theorem states that if $a+bi$ is a zero of a polynomial function with real coefficients, then $a-bi$ is also a zero of the function. The given statement is false since having $i$ and $3+i$ as zeros of a polynomial function with real coefficients means that $-i$ and $3-i$ are also zeros of the function. However, since the polynomial function's degree is three, it only has three zeros.
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