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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, then find the sum of a and b.

 May 1, 2022
 #1
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For rational functions, asymptotes occur when the denominator is 0.

 

Then x = 1 and x = 2 are roots of x^2 + ax + b = 0.

 

Using some precalculus, a = -3 and b = 2.

 

The value of a + b is obvious at this point.

 May 2, 2022

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