Chapter 3.1, Problem 19E

To determine

To calculate: The roots of the equation $\frac{1}{2}{r}^2-10=\frac{3}{2}{r}^2$ .

Answer to Problem 19E

The roots of the equation are $-i\sqrt{10}\text{and}i\sqrt{10}$ .

Explanation of Solution

Given information:

The given equation $\frac{1}{2}{r}^2-10=\frac{3}{2}{r}^2$ .

Calculation:

Consider the given equation is $\frac{1}{2}{r}^2-10=\frac{3}{2}{r}^2$ .

Now, solve the solve expression for $r$ .

  $\begin{array}{c}\frac{1}{2}{r}^2-10=\frac{3}{2}{r}^2\\ \frac{1}{2}{r}^2-\frac{3}{2}{r}^2=10\\ -\frac{2}{2}{r}^2=10\\ r^2=-10\\ r=\sqrt{-10}\\ =\pm i\sqrt{10}\end{array}$

Hence, the roots of the equation are $-i\sqrt{10}\text{and}i\sqrt{10}$ .