Chapter 9, Problem 20CCSR

To determine

To determine the number of real number solutions of given quadratic equation.

Answer to Problem 20CCSR

There are zero real solutions.

Explanation of Solution

Given information:

  $2x^2+7x+9=0$

Here we shall determine the value of $x.$

  $\begin{array}{l}x=\frac{-7\pm \sqrt{7^2-4\left(2\right)\left(9\right)}}{2\left(2\right)}\\ x=\frac{-7\pm \sqrt{-33}}{4}\end{array}$

We can observe that the discriminant of the given equation is negative.

Hence the roots of the equation are imaginary numbers.

Therefore there are zero real solutions.