# How do you find the zeros of the function #f(x)=(x^2+3x-4)/(x^2+9x+20)#?

##### 1 Answer

Dec 3, 2017

By finding the zeros of the numerator and checking if they do not occur in the denominator. Here we have x=1 as zero.

#### Explanation:

This is a rational function (a polynomial divided by another polynomial). The zeros of a rational function are the zeros of the numerator polynomial, provided that they do not occur in the denominator polynomial. If the zero is a zero of both numerator and denominator, we divide the common factor away to resolve the limit because then we have 0/0 which has to be resolved by limits.

So in this case we have

So the zero -4 occurs in the numerator and denominator so we divide the common factor away and are left with :

So the zero is x=1.

Answer x=1 is the only true zero.