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JEE MAIN 2021
25-02-2021 S2
Question
If $a, \beta \in R$ 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:
Select the correct option:
A
3
B
7
C
7
D
3
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
- $\alpha, \beta \in \mathrm{R} \Rightarrow$ other root is $1+2 i$ $$ \begin{aligned} & \alpha=- \text { (sum of roots) }=-(1-2 i+1+2 i)=\square 2 \\ & \beta=\text { product of roots }=(1 \square 2 i)(1+2 i)=5 \\ & \therefore \quad \alpha-\beta=-7 \end{aligned} $$
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