Consider the quadratic equation $(a+c-b)x^2 + 2cx + b+c-a = 0 $ , where a,b,c are distinct real numbers and a+c-b is not equal to 0. Suppose that both the roots of the equation are rational . Then a) a,b, and c are rational
b)$c/(a-b)$ is rational
c)$b/(c-a)$ is rational
d)$a/(b-c)$ is rational
My attempt - I used the discriminant method to find out the possible roots of the given equation. Which for me came out to be $(-2c + a-b)/(2a -2b +2c)$ and $ ( -2c + b - a)/(2c + 2a - 2b )$
Hence according to me option a is the correct answer , while the correct answer which is given is b. Please tell me where am I going wrong , or what am I missing ?