JEE Main 2021 (Online) 25th February Evening ShiftQuestion 1
If $\alpha,\beta\in\mathbf{R}$ are such that $1-2i$ (here $i^{2}=-1$) is a root of $z^{2}+\alpha z+\beta=0$, then $(\alpha-\beta)$ is equal to :
Complex Numbers
Solution
Roots are $1\mp2i$: sum $2=-\alpha\Rightarrow\alpha=-2$; product $5=\beta$. $\alpha-\beta=-7$. Option (D).