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: 45

Answer

Having $2+i$ as a zero means that its conjugate $2-i$ must also be a zero 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 $2+i$ as a zero of a polynomial function with real coefficients means that $2-i$ is also a zero of the function.
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