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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 \(b\).

 Jun 29, 2018
 #1
avatar+101360 
+2

  x + 4

__________

x^2 + ax + b

 

If the vertical asymptotes are   x  =1  and x = -2....the denominator  is

 

( x - 1)  ( x +  2)   =  x^2  + x  -  2

 

So.....

 

a =  1    and b  = -2

 

So....a +  b  =   1  +  (-2)  =   -1

 

 

cool cool cool

 Jun 29, 2018

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