College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding: 39

Answer

$\pm9,\pm3,\pm\frac{3}{2},\pm 1;\pm\frac{1}{2},\pm \frac {1}{3},\pm\frac{9}{2},\pm\frac{1}{6}$

Work Step by Step

In a polinomial function like $f\left( x\right) =a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots a_{1}x+a_{0}$ If $p/q$, in lowest terms, is a rational zero of $f$, then p must be a factor of $a_0 $ and $q$ must be a factor of $a_n$. Here $f\left( x\right) =6x^{4}-x^{2}+9\Rightarrow a_{n}=6;a_{0}=9 $ Factors of $a_0$ are $\pm 1,\pm3,\pm9$ Factors of $a_n$ are $\pm1 ,\pm2, \pm3,\pm6$ So the potential rational zeros are: $\pm9,\pm3,\pm\frac{3}{2},\pm 1;\pm\frac{1}{2},\pm \frac {1}{3},\pm\frac{9}{2},\pm\frac{1}{6}$
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