Posted by **hmmm** on Monday, April 29, 2013 at 11:46am.

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.

- algebra -
**Steve**, Monday, April 29, 2013 at 2:32pm
You sure these are < and >, not <= and >=?

Solutions to such are open intervals.

Intersections of open intervals cannot be a single value for x.

- algebra -
**hmmm**, Tuesday, April 30, 2013 at 2:35am
ohw... sorry for that... for clarification, it's:

{(c-1)x^2+2cx+c+4<or=0

{ cx^2 + 2(c+1)x+(c+1)>or=0

- algebra -
**pi**, Wednesday, May 1, 2013 at 6:50am
5/4. Giving 9

- algebra -
**Math defender**, Thursday, May 2, 2013 at 11:35am
no, its incorrect

- algebra -
**hans**, Tuesday, May 7, 2013 at 1:41am
19 is the correct answer

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