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 240: 27

Answer

$3+2i,-2,5$

Work Step by Step

Step 1. Given a zero $x=3-2i$, we know another zero is $x=3+2i$, thus $(x-3+2i)(x-3-2i)=x^2-6x+13$ is a factor. Step 2. Perform a division as shown in the figure to get the quotient $x^2-3x-10$ (one can also perform synthetic divisions to get the same result). Step 3. Solve $x^2-3x-10=0$ or $(x+2)(x-5)=0$ to get $x=-2,5$
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