Question

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

Answer 1

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
`f(x) = ((x+4)(x-1))/((x+5)(x+4))`
So the zero -4 occurs in the numerator and denominator so we divide the common factor away and are left with :
`f(x) = (x-1)/(x+5)`
So the zero is x=1.
Answer x=1 is the only true zero.