Chapter A.7, Problem 78AYU

To determine

To explain:The character of solution of given equation in complex number system.

Explanation of Solution

Given information:

The equationis $4x^2+12x+9=0$ .

Calculation:

Consider the equation.

  $4x^2+12x+9=0$

Check for $b^2-4ac$ ,

  $\begin{array}{c}{\left(12\right)}^2-4\left(4\right)\left(9\right)=144-144\\ =0\end{array}$

As $b^2-4ac=0$ , there is a repeated real solution.