College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.6 - Page 420: 28


Solution set: $(-\infty,\infty).$

Work Step by Step

Follow the "Procedure for Solving Polynomial lnequalities",\ p.412: 1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$ where $f$ is a polynomial function. $4x^{2}-4x+1\geq 0$ We recognize the LHS as a square of a difference... $(2x-1)^{2} \geq 0$ ... We do not need to follow the steps any further, since this inequality asks: "For which real numbers is a square nonnegative?" The answer: "Always (for all x$\in \mathbb{R}$)." Solution set: $(-\infty,\infty).$
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