Which of the following represents the vertical asymptotes of the function f(x)= x/ x^2 - 2x - 8 ?

Question

anonymous · Answer

@Michele_Laino

anonymous · Answer

A. x = -8 and x =1 	
  B. x= -1 and x = 8 	
  C. x = -4 and x = 2 	
  D. x = -2 and x = 4 
Those are my choices.

michele_laino · Answer

vertical asymptotes are positioned at values of $x$, such that the denominator is equal to zero, so, we have to solve this quadratic equation:

$\huge  x^2-2x-8=0$

anonymous · Answer

How do I do that?

michele_laino · Answer

do you know how to solve a quadratic equation?

anonymous · Answer

no..):

michele_laino · Answer

in that case, we can solve such equation, in another way, namely, you have to search, among your options, two numbers, such that their product is equal to $-8$, and their sum is equal to $2$

anonymous · Answer

Like out of my choices?

michele_laino · Answer

for example, first option gives,  -8, and 1, now:
sum = -8+1= -7 which is different from 2, so option A, is a wrong option

anonymous · Answer

I say C.

anonymous · Answer

D*

michele_laino · Answer

I think C is wrong since we have -4, and 2, and:
sum = -4+2=-2 which is different from 2

michele_laino · Answer

option D is the correct option! :)