Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.5 Inequalities Involving Quadratic Functions - 3.5 Assess Your Understanding - Page 160: 19


The solution set is empty.

Work Step by Step

$4x^2+9<6x$, I subtract $6x$ from both sides, hence $4x^2-6x+9<0$, its determinant ($b^2-4ac=(-6)^2-4\cdot4\cdot9=-108$) is less than $0$, hence it cannot be less than $0$ (also because its leading coefficient, $4$ is bigger than $0$), hence the solution set is empty. (also see the graph of $4x^2-6x+9$)
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