The discriminant is
Then the roots are:
Then must be rational.
consider a quadratic equation (a+c-b)x^2 + 2cx + (b+c-a) = 0, where a,b,c are distinct real numbers and a+b-c is not equal to 0. Suppose that both the roots of the equation are rational. Then which must hold true?
1. a,b,c are rational
2. c/(a-b) are rational
3. b/(c-a) are rational
4. a / (b-c) are rational.