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.

Guest Sep 24, 2022

#1**0 **

*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 x^{2} + 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 x^{2} + 1x – 2

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

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Guest Sep 24, 2022