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: 14

Answer

$x=\{ -4,2 \}$

Work Step by Step

The two numbers whose product is $ac=1(-8)=-8 $ and whose sum is $b= 2 $ are $\{ 4,-2 \}$. Using these two numbers to decompose the middle term of the given equation, $ x^2+2x-8=0 ,$ results to \begin{array}{l}\require{cancel} x^2+4x-2x-8=0 \\\\ (x^2+4x)-(2x+8)=0 \\\\ x(x+4)-2(x+4)=0 \\\\ (x+4)(x-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+4=0 \\\\ x=-4 ,\\\\\text{OR}\\\\ x-2=0 \\\\ x=2 .\end{array} Hence, the solutions are $ x=\{ -4,2 \} .$
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