Chapter 6.1, Problem 23WE

To determine

The real roots of the equation $4-16x^2=0$ , if there are no such roots say so.

Answer to Problem 23WE

The real roots of the equation are $x=\pm \frac{1}{\sqrt{2}}$ .

Explanation of Solution

Given information: The given equation is,

  $4-16x^2=\mathrm{0......}\left(1\right)$

Calculation: Simplify (1),

  $\begin{array}{c}4-16x^2=\mathrm{0......}\left(\text{Given}\right)\\ \text{or, }16x^2=4\\ x^2=\frac{1}{4}\\ x=\pm \sqrt{\frac{1}{4}}\\ x=\pm \frac{1}{\sqrt{2}}\end{array}$