Question

Help pls! Which rational function has zeros at x = -1 and x = 6 ?

Answer 1

Answer:

$f(x) = \frac{x^{2} -5x-6}{x^{2} -4}$

Step-by-step explanation:

Let's factorize the 1st option :

⇒ $f(x) = \frac{x^{2} -5x-6}{x^{2} -4}$

⇒ $f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}$

⇒ $f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}$

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Finding the zeros :

⇒ Factors of numerator should be equated to 0

1. x + 1 = 0 ⇒ x = -1
2. x - 6 = 0 ⇒ x = 6

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Solution :

$f(x) = \frac{x^{2} -5x-6}{x^{2} -4}$

Answer 2

Answer:

first option

Step-by-step explanation:

the zeros are determined by the numerator of the rational function.

given that the zeros are x = - 1 and x = 6 , then the corresponding factors are

(x + 1) and (x - 6) , that is

(x + 1)(x - 6) ← expand using FOIL

= x² - 5x - 6

the rational function is then

f(x) = $\frac{x^2-5x-6}{x^2-4}$