Given, root of z2+αz+β=0 is 1−2i. Since, it is quadratic equation and one root is complex in nature, its another root is complex conjugate. ∴ Two roots are 1−2i and 1+2i. Now, sum of roots =−‌
α
1
=−α =(1−2i)+(1+2i)=2 Gives, α=−2 Product of roots =‌