Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 379: 73

Answer

The graph is shown below:
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Work Step by Step

The constant term of the polynomial $f\left( x \right)$ is: ${{a}_{0}}=-4$ This gives the possible factors of ${{a}_{0}}$: $p=1,2,4$ The coefficient of the term with the highest power of the polynomial $f\left( x \right)$ is: ${{a}_{n}}=6$ This gives the possible factors of ${{a}_{n}}$: $q=1,2,3,6$ Therefore, using the rational zero theorem the possible rational zeros of the functions are: $r\,\,=\,\,\pm 1,\,\,\pm 2,\,\,\pm 4,\,\,\pm \frac{1}{2},\,\,\pm \frac{2}{2},\,\,\pm \frac{4}{2},\,\,\pm \frac{1}{3},\,\,\pm \frac{2}{3},\,\,\pm \frac{4}{3},\,\,\pm \frac{1}{6},\,\,\pm \frac{2}{6},\,\,\pm \frac{4}{6}$ Therefore, the rational zeros of the functions are $r=\frac{1}{2},\,\,\frac{2}{3},\,\,2$.
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