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

Tabitha Doyle

Tabitha Doyle

Answered question

2022-09-27

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

Answer & Explanation

Lamar Esparza

Lamar Esparza

Beginner2022-09-28Added 8 answers

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.

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