College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 388: 61

Answer

$x\displaystyle \in\{-\sqrt{5},\ \frac{1}{3}, \ \sqrt{5}\}$

Work Step by Step

Factor in pairs $x^{2}(3x-1)-5(3x-1)=0$ $(3x-1)(x^{2}-5)=0\qquad$ ... difference of squares $(3x-1)(x+\sqrt{5})(x-\sqrt{5})=0$ $3x-1=0\ \ \displaystyle \Rightarrow\ \ x=\frac{1}{3}, $ $x\displaystyle \in\{-\sqrt{5},\ \frac{1}{3}, \ \sqrt{5}\}$
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