College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.4 - Page 389: 75

Answer

Possible rational roots: $ \displaystyle \pm 1,\pm 2,\pm\frac{1}{2},\pm\frac{1}{4}$ Actual rational roots: $-\displaystyle \frac{1}{2}$ and $\displaystyle \frac{1}{2}.$ (see image below)
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Work Step by Step

By the Rational Zero Theorem, if there is a rational root$, \displaystyle \frac{p}{q}$, of a polynomial equation, then p is a factor of the constant term, $a_{o}$ and q is a factor of the coefficient of the leading term $a_{n}$. ---------- $p:\quad \pm 1,\pm 2$ $q:\quad \pm 1,\pm 2,\pm 4$ $\displaystyle \frac{p}{q}:\quad \pm 1,\pm 2,\pm\frac{1}{2},\pm\frac{1}{4}$ As a graphing utility, I used desmos.com online calculator. Adjust the viewing window and step with the dialog box that opens when we press the "wrench" button in the right upper corner (see image below) On the resulting graph, we see that actual roots are $-\displaystyle \frac{1}{2}$ and $\displaystyle \frac{1}{2}.$
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