College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises - Page 112: 15


$x=\left\{ -\dfrac{2}{5},1 \right\}$

Work Step by Step

The two numbers whose product is $ac= 5(-2)=-10 $ and whose sum is $b= -3 $ are $\{ -5,2 \}$. Using these two numbers to decompose the middle term of the given equation, $ 5x^2-3x-2=0 ,$ results to \begin{array}{l}\require{cancel} 5x^2-5x+2x-2=0 \\\\ (5x^2-5x)+(2x-2)=0 \\\\ 5x(x-1)+2(x-1)=0 \\\\ (x-1)(5x+2)=0 .\end{array} Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are \begin{array}{l}\require{cancel} x-1=0 \\\\ x=1 ,\\\\\text{OR}\\\\ 5x+2=0 \\\\ 5x=-2 \\\\ x=-\dfrac{2}{5} .\end{array} Hence, the solutions are $ x=\left\{ -\dfrac{2}{5},1 \right\} .$
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