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Please help me with this problem.

 

\(\text{If $f(x)=\frac{x+4}{x^2+ax+b}$, and $f(x)$ has two vertical asymptotes at $x=1$ and $x=-2$, find the sum of $a$ and $b$. }\)

 

Thanks!

 Jul 16, 2019
 #1
avatar+111393 
+1

Since we have vertical asymptotes at  x  = 1  and x  = - 2, the denominator has the form

 

(x - 1) (x + 2)    since  x = 1  and x  = -2   will make the denominator 0

 

So....expanding....we  have   x^2 -  1x  + 2x  - 2  =  x^2 + 1x  - 2 = x^2 + ax + b

 

So

 

a  =1     and b   =-2

 

And  a + b  =  1 + (-2)  =   -1

 

 

cool cool cool

 Jul 16, 2019
 #2
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+1

Thanks a lot!! laugh

 Jul 16, 2019

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