Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 241: 44


The function has $5$ zeros so its degree is $5$, not $3$.

Work Step by Step

The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. Since $2$, $i$ and $(3+i)$ are zeros of $f(x)$, then $\overline{i}=-i$ and $\overline{3+i}=3-i$ are also zeros of $f(x)$. Thus, $f(x)$ has $5$ zeros which means that its degree is $5$.
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