Chapter 4.7, Problem 10OE

To determine

To solve: the polynomial

Answer to Problem 10OE

The value of $4x^2-1=0$ is $x=\left\{-\frac{1}{2},\frac{1}{2}\right\}$

Explanation of Solution

Given information: The polynomial is $4x^2-1=0$

Calculation:

  $\begin{array}{l}4x^2-1=0\\ {\left(2x\right)}^2-1^2=0\\ \left(2x+1\right)\left(2x-1\right)=0\end{array}$

The given equation already has $0$ as one side, and the other side is already factored

Simplify set each factor equal to $0$

  $\begin{array}{l}2x+1=0\\ 2x=-1\\ x=-\frac{1}{2}\\ 2x-1=0\\ 2x=1\\ x=\frac{1}{2}\\ x=\left\{-\frac{1}{2},\frac{1}{2}\right\}\end{array}$