Question
Consider the following system of inequalities:
(c−1)x^2+2cx+c+4≤0 ---- (1)
cx^2+2(c+1)x+(c+1)≥0 ---- (2)
The sum of all real values of c, such that the system has a unique solution, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
Details and assumptions
c can be negative.
The system has a unique solution if there is only 1 real value x which is satisfied throughout.
(c−1)x^2+2cx+c+4≤0 ---- (1)
cx^2+2(c+1)x+(c+1)≥0 ---- (2)
The sum of all real values of c, such that the system has a unique solution, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
Details and assumptions
c can be negative.
The system has a unique solution if there is only 1 real value x which is satisfied throughout.