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The graph of f(x) = (2x)/(3x^2 - 6x - 14) has vertical asymptotes x = a and x = b, and horizontal asymptote y = c. Find a + b + c.

 Jul 27, 2022
 #1
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(2x)  / ( 3x^2  - 6x  - 14)

 

We have a lower  power polynomial  over a higher power polynomial......this sets up a horizontal asymptote at y = 0

 

The vertical  asymptotes  will be where    3x^2 - 6x - 14  = 0

 

By Vieta   the sum of the asymptotes  =   the sum of the roots of this poynomial  =   a  + b  =    - (-6) / 3   = 2

 

So

 

a +  b +  c   =   0 +  2   = 2

 

 

cool cool

 Jul 27, 2022

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