Chapter 9.6, Problem 11CYU

To determine

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

Answer to Problem 11CYU

The equation has no real solutions

Explanation of Solution

Given:

  $\text{Equation:}{x}^2-9x+21=0$

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:}{x}^2-9x+21=0\\ a=1;b=-9;c=21\\ $ \text{discriminant}:b^2-4ac={(-9)}^2-4·1·21=81-84=-3$\end{array}$

Discriminant is − 3.

Since the discriminant is negative, the equation has no real solutions.

Thus, the equation has no real solutions