If α,β∈R  are such that 1−2i(here  i2=−1) is a root of z2+αz+β=0,then  (α−β) is equal to

Given z2+αz+β=0  has one root 1 – 2i            Hence, the other root is conjugate of the other   ( since the coefficients α ,β are real ), then the other root is 1 + 2i            Therefore,  sum of the roots =-α=2;  and product of the roots =  β=1+2i1-2i=5 ⇒α−β=−2−5=−7