Chapter 12.2, Problem 40SR

To determine

To find: Zeroes of the function.

Answer to Problem 40SR

The zeroes of the function is 3, 5.

Explanation of Solution

Given information:

The function is $f\left(x\right)=\frac{x^2-8x+15}{x^2+5x-6}$ .

Calculation:

Since the roots can be found by setting the equation as zero, that is, $f\left(x\right)=0$ .

First, factorize the numerator and denominator to cancel the common factors to eliminate possible extraneous solution that makes the function undefined. Therefore,

  $f\left(x\right)=\frac{\left(x-5\right)\left(x-3\right)}{\left(x+6\right)\left(x-1\right)}$

As there are no common factors substitute $f\left(x\right)=0$ and solve for $x$ :

  $\begin{array}{l}\frac{\left(x-5\right)\left(x-3\right)}{\left(x+6\right)\left(x-1\right)}=0\\ \left(x-5\right)\left(x-3\right)=0\text{ (Since }\left(x+6\right)\left(x-1\right)\ne 0\text{)}\\ x=3,\text{ 5}\end{array}$

Hence,

The zeroes of the function is 3, 5.