College Algebra (10th Edition)

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

Chapter 4 - Section 4.5 - Inequalities involving Quadratic Functions - 4.5 Assess Your Understanding - Page 314: 14

Answer

The inequality is valid for values between -4 and -3 (not including them) i.e. $(-4,-3)$

Work Step by Step

First, we are going to set the right side to zero and factor to find the x-intercepts: $x^2+7x+12=0$ $(x+4)(x+3)=0$ $x_1=-4$ $x_2=-3$ These are the critical points. We are going to take three values: one less than -4, one between -4 and -3, and one more than -3 to test in the original equation and check if the inequality is true or not: First test with a value less than -4: $(-5)^2+7(-5)
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