Consider the following system of inequalities:

{(c−1)x^2+2cx+c+4≤0
cx^2+2(c+1)x+(c+1)≥0
The sum of all real values of c, such that the system has a unique solution, can be written as ab, 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.

2 answers

19

thanx

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