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: 9

Answer

The inequality is valid on values less than 0 and more than 4 (not including them) i.e. $(-\infty,0)\cap (4,\infty)$

Work Step by Step

First, we are going to set the right side to zero and factor to find the x-intercepts: $x^2-4x$ $x(x-4)$ $x_1=0$ $x_2=4$ These are the critical points. We are going to take three values: one less than 0, one between 0 and 4, and one more than 4 to test in the original equation and check if the inequality is true or not: First test with a value less than 0: $(-1)^2-4(-1)>0$ $1+4>0$ $5>0 \rightarrow \text{ TRUE}$ Second test with a value between 0 and 4: $1^2-4(1)>0$ $1-4>0$ $-3>0 \rightarrow \text{ FALSE}$ Third test with a value more than 4: $5^2-4(5)>0$ $25-20>0$ $5>0 \rightarrow \text{ TRUE}$ These tests show that the inequality $x^2-4x>0$ is valid on values less than 0 and more than 4 (not including them) i.e. $(-\infty,0)\cap (4,\infty)$
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