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.
+128475 A vertical asypmtote occurs when an x value makes the denominator = 0
So we have that
x^2 + ax + b = 0
And we know that the roots of this = 1 , 2
By Vieta
The sum of the roots = -a
So
1 + 2 = -a
3 = -a
a = -3
And the product of the roots = b
So
1*2 = b
2 = b
a + b = -3 + 2 = -1
