if has but 2 real roots, then must have but 1 real root, so its discriminant:
since we have that:
EDIT: upon further reflection, and seeing ProveIt's answer, it's clear that although this condition is necessary, it is not sufficient, because u must be non-negative for x to be real.
this means that u = -(2a+b)/2a when Δ = 0. unfortunately, if we do not know if a > 0, we cannot decide if we should have 2a+b > 0, or 2a+b < 0.
one thing is certain, however, if b = -2a, then we only have one root for x.