Chapter 9.5, Problem 27E

To determine

To find the number of real solutions of the Quadratic equation.

Answer to Problem 27E

One real solutions of the equation.

Explanation of Solution

Given:

Equation:

  $2x^2-12x=-18$

Formula used:

Discriminant formula.

  $D=b^2-4ac$

Calculation:

Converting the equation in standard form

  $2x^2-12x+18=0$

On comparing the equation with $a{x}^2+bx+c$

  $a=2,b=-12,c=18$

Finding the value of $D$

  $D=b^2-4ac$

Substituting the values,

  $D={(-12)}^2-4(2)(18)$

Opening brackets,

  $D=144-144$

So,

  $D=0$

Since, $D$ is zero.

Therefore, there will be one real solutions of the equation.