Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.3 Studying Solutions of Quadratic Equations - 11.3 Exercise Set - Page 718: 38



Work Step by Step

$x=\displaystyle \frac{1}{2}$ or $ x=\displaystyle \frac{1}{3}\qquad$....get $0$'s on one side. $x-\displaystyle \frac{1}{2}=0$ or $ x-\displaystyle \frac{1}{3}=0\qquad$....Use the principle of zero products (multiplying). The solutions of this equation are $\displaystyle \frac{1}{2}$ and $\displaystyle \frac{1}{3}$. $(x-\displaystyle \frac{1}{2})(x-\frac{1}{3})=0\qquad$...use the FOIL method to multiply. $ x^{2}-\displaystyle \frac{1}{3}x-\frac{1}{2}x+\frac{1}{6}=0\qquad$...combine like terms. $ x^{2}-\displaystyle \frac{5}{6}x+\frac{1}{6}=0\qquad$...multiply both sides by $6$ to clear fractions. $6x^{2}-5x+1=0$
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