Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.4 - Real Zeros of Polynomials - 3.4 Exercises - Page 283: 14

Answer

a. $ \quad \displaystyle \pm 1, \pm\frac{1}{2}, \pm\frac{1}{4}.$ b. $\quad \displaystyle \frac{1}{4}, 1$

Work Step by Step

If $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ has integer coefficients, then all the rational zeros of $P$ have the form $x=\displaystyle \pm\frac{p}{q}$ where $p$ is a divisor of the constant term $a_{0}$ and $q$ is a divisor of the leading coefficient $a_{n}$. ----------- a. $a_{0}=1 \qquad $p: $\pm 1,$ $a_{n}=4,\qquad $q: $\pm 1, \pm 2,\pm 4$ Possible $\displaystyle \frac{p}{q}:\quad \pm 1, \pm\frac{1}{2}, \pm\frac{1}{4}.$ b. From the graph, actual zeros (x-intercepts): $\displaystyle \frac{1}{4}, 1$
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