Solve Quadratic Equations: Find |a-b| for n=a,b

[erisedk]

Homework Statement

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

Homework Equations

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?

 

[jedishrfu]

Can you subtract the b version from the a version, simplify and then see if you can get the absolute value answer?

Perhaps the absolute value trick of using the square root will help?

abs(x) = sqrt(x^2)