Chapter 4.2, Problem 5CYU

To determine

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

Answer to Problem 5CYU

  $x=0,x=-8$ .

Explanation of Solution

Given:

The given equation is $x^2-3x-18=0$ .

Calculation:

The given equation is $x^2-3x-18=0$ .

Now, solve the given equation by factor method. Therefore,

  $\begin{array}{l}{x}^2-3x-18=0\left\{\text{given function}\right\}\\ x^2-6x+3x-18=0\{\text{simplify}}\\ x\left(x-6\right)+3\left(x-6\right)=0\{\text{factor}}\\ \left(x+3\right)\left(x-6\right)=0\{\text{obtain the factor}}\end{array}$

Therefore, either $\left(x+3\right)=0$ or $\left(x-6\right)=0$

When $\left(x+3\right)=0$ , then $x=-3$ .

And When $\left(x-6\right)=0$ , then $x=6$ .

Thus, the zeros of the function are $x=-3,x=-6$ .

Hence, the solution of the given equation is $x=0,x=-8$ .