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 233: 36

Answer

$\pm1,\pm\frac{1}{2}$

Work Step by Step

If $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient, then the potential zeros can be gained by the possible combinations in $\frac{p}{q}$. The given polynomial function has a constant term of $1$ and a leading coefficient of $2$. The possible factors $p$ of the constant term and $q$ of the leading coefficient are: $p=\pm1$ $q=\pm1,\pm2$ Thus, the possible rational roots of $f(x)$ are: $\frac{p}{q}=\pm1,\pm\frac{1}{2}$
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