Chapter 5.2, Problem 42PPS

To determine

To solve: the given equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.

Answer to Problem 42PPS

  $x=1.5,x=-4$ .

Explanation of Solution

Given:

The given equation is $-5x-12=-2x^2$ .

Calculation:

The given equation is expressed as $2x^2-5x-12=0$ .

As the standard form of the equation is $a{x}^2+bx+c=0$

Now, to find the zeros of the given equation by using determinant method. Therefore,

  $\begin{array}{l}X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\left\{\text{determinant formula}\right\}\\ X=\frac{-5\pm \sqrt{{\left(-5\right)}^2-4\left(2\right)\left(-12\right)}}{2\left(2\right)}\{\text{substitues the value}}\\ X=\frac{-5\pm \sqrt{25-\left(-96\right)}}{4}\{\text{simplify}}\\ X=\frac{-5\pm \sqrt{121}}{4}=\frac{-5\pm 11}{4}\end{array}$

Therefore, either $x_1=\frac{-5+11}{4}$ or $x_2=\frac{-5-11}{4}$

When $x_1=\frac{-5+11}{4}$ , then $x=1.5$ .

When $x_2=\frac{-5-11}{4}$ , then $x=-4$ .

Thus, the zeros of the function are $x=1.5,x=-4$ .

Hence, the solution of the given equation is $x=1.5,x=-4$ .