#
prove that roots of (x-a)(x-b)=h^{2} are always real.

Coefficient of x^2 ie. a = 1

Constant term .i.e c = ab - h^2

Discriminant

b^2 - 4 a c

(a+b)^2 - 4ab + h^2 = (a - b)^2 + h^2

So it seems the discriminant is always positive i.e D > 0

Hence only real roots. PROVED