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 - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 234: 64

Answer

$\{1,1\}$

Work Step by Step

Step 1. Given $f(x)=x^4-2x^3+10x^2-18x+9$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm3,\pm9$ Step 2. Use synthetic division as shown in the figure to find zeros $x=1,1$. Step 3. Use the quotient and solve $x^2+9=0$ and there are no real zeros. Step 4. Thus the real zeros are $\{1,1\}$
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