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: 13

Answer

$a.\displaystyle \quad\pm 1,\pm 3,\pm\frac{1}{2},\pm\frac{3}{2}$ $b.\displaystyle \quad-\frac{1}{2},1,$ and $3$

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 $a_{n}$ --- $a.$ $P(x)=2x^{4}-9x^{3}+9x^{2}+x-3$ candidates for p: $\pm 1,\pm 3$ candidates for q: $\pm 1,\pm 2$ Possible rational zeros $\displaystyle \frac{p}{q}$:$\displaystyle \quad \pm 1,\pm 3,\pm\frac{1}{2},\pm\frac{3}{2}.$ $b.$ From the graph, the actual zeros are $-\displaystyle \frac{1}{2},1,$ and $3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.