# 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: $(-\infty,\infty).$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.