If 1-2i is a root of the equation z2+αz+β=0 where α,β∈R then the value of α−β is

It is given that a=1−2i is a root of z2+αz+β=0 and imaginary roots of an equation with real coefficients occur in conjugate pairs. Therefore, the order root is b = 1 + 2i.⇒a+b=2 and ab=5⇒−α=2 and β=5⇒α−β=−7