Chapter 9.6, Problem 13CYU

To determine

Find the value of the discriminant and determine the number of real solution of the equation.

Answer to Problem 13CYU

The equation has one real solution.

Explanation of Solution

Given:

  $\text{9}{x}^2+24x=-16$

Concept Used:

  $\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac$

Calculation:

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac\\ \text{Equation:}\text{9}{x}^2+24x=-16\\ \text{Standard}\text{Form}:\text{9}{x}^2+24x+16=0\\ a=9;b=24;c=16\\ $ \text{discriminant}:b^2-4ac={(24)}^2-4·9·16=576-576=0$\end{array}$

Discriminant is 0.

Since the discriminant is zero, the equation has one real solution.

Thus, the equation has one real solution.