The solution to the inequality \(\frac{x + c}{x^2 + ax + b} \le 0\) is \(x \in (-\infty,-1) \cup [1,2)\).Find a + b + c.
+130536 Since the interval [ 1 , 2) makes this true, then x = 1 is a root and ( x - 1) must be the linear factor in the numerator
Since the function is true for (-inf, -1) and [1, 2)
We might guess that we have vertical asymptotes at x = -1 and x = 2
So.... (x + 1) and (x - 2) seem to be linear factors in the denominator
And our function is ( x - 1) ( x - 1)
___________ = ___________
(x + 1) ( x -2) x^2 - x - 2
See the graph here : https://www.desmos.com/calculator/dhotlrocam
Note that y is ≤ 0 on the intervals (-inf, -1) U [ 1, 2 )
So a = -1 b = -2 and c = -1
And their sum is - 4
