1. The problem statement, all variables and given/known data If roots of the equation x^2 - (2n+18)x - n - 11 = 0 (n is an integer) are rational for n=a and n=b then |a-b| is Ans: 3 2. Relevant equations 3. The attempt at a solution On substituting a (or b) into the quadratic, the roots are rational. If the roots are rational, then the discriminant must be a perfect square (and positive). Hence, (2a+18)^2 + 4(a+11) = k^2 On simplifying, a^2 + 19a + 92 = k^2 and a^2 + 19a + 92 > 0 What do I do after this?