College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.4 - Real Zeros of Polynomials - 3.4 Exercises - Page 319: 11


$a.\displaystyle \quad\pm 1,\pm\frac{1}{5}$ . $b.\displaystyle \quad-1,\frac{1}{5},$ and $1$

Work Step by Step

Rational Zeros Theorem$:$ $ ... $every rational zero of $P(x)$ is of the form $\displaystyle \frac{p}{q}$ where $p$ and $q$ are integers and $p$ is a factor of the constant coefficient $a_{0}$ $q$ is a factor of the leading coefficient $a_{n}$ --- $a.$ $P(x)=5x^{3}-x^{2}-5x+1$ candidates for p: $\pm 1,$ candidates for q: $\pm 1,\pm 5$ Possible rational zeros $\displaystyle \frac{p}{q}:\quad $$\displaystyle \pm 1,\pm\frac{1}{5}$ . $b.$ From the graph, the actual zeroes are $-1,\displaystyle \frac{1}{5},$ and $1.$
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