Question:
If $\alpha, \beta \in R$ are such that $1-2 i$ (here $i^{2}=-1$ ) is a root of $z^{2}+\alpha z+\beta=0$, then $(\alpha-\beta)$ is equal to :
Correct Option: , 2
Solution:
$\because \alpha, \beta \in \mathrm{R} \Rightarrow$ other root is $1+2 \mathrm{i}$
$\alpha=-($ sum of roots $)=-(1-2 \mathrm{i}+1+2 \mathrm{i})=-2$
$\beta=$ product of roots $=(1-2 \mathrm{i})(1+2 \mathrm{i})=5$
$\therefore \alpha-\beta=-7$
option (2)
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.