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: 46

Answer

One of the missing zeros is $4+i$. The fourth zero must be a real number. The fourth zero cannot be a complex number since complex zeros come in pairs.

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 function's degree is four so it has four zeros. Having $4-i$ as z zero of the given function means $4+i$ is also a zero of the function. Thus, three of the function's four zeros are $-3, 4-i, 4+i$. This means that the fourth zero cannot be a complex number since complex zeros come in pairs. Therefore, the fourth zero must be a real number.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.