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If f(x)=(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.

 Sep 24, 2022
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If f(x)=(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.  

 

You get an asymptote when the denominator is zero. 

 

The denominator is x2 + ax + b     This is a quadratic equation, and a  

                                                      quadratic equation has two solutions. 

 

The problem itself tells us where the asymptotes are, thus it tells us what the solutions are.  

 

Since the asymptotes occur at  x = 1 and x = –2  then the factors of that  

quadratic equation are            (x – 1) and (x + 2)  which multiplies out to  x2 + 1x – 2  

 

So a + b  which is  [ (+1) + (–2) ]  equals  –1  

.

 Sep 24, 2022

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