College Algebra (10th Edition)

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

Chapter 5 - Section 5.6 - Complex Zeros; Fundamental Theorem of Algebra - 5.6 Assess Your Understanding: 6

Answer

False

Work Step by Step

The given fourth degree polynomial function has the following zeros: $-3 \\2+i \\2-i \\-3+5i$ The Conjugate Pairs Theorem states that if $a+bi$ is a zero of a polynomial function with a real number of coefficients, then $a-bi$ is also a zero of the function. This means that since $-3+5i$ is a zero of the given function, $-3-5i$ is also a zero of the function. Since $-3-5i$ is not listed as a zero of the fourth-degree polynomial function, the given statement is false.
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