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.
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
.