Chapter 9.6, Problem 14CYU

To determine

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

Answer to Problem 14CYU

The equation has two real solutions.

Explanation of Solution

Given:

  $\text{Equation:}\text{3}{x}^2-x=8$

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{3}{x}^2-x=8\\ \text{Standard}\text{Form}:\text{3}{x}^2-x-8=0\\ a=3;b=-1;c=-8\\ $ \text{discriminant}:b^2-4ac={(-1)}^2-4·3·-8=1+96=97$\end{array}$

Discriminant is positive.

Since the discriminant is positive, the equation has two real solutions.

Thus, the equation has two real solutions.