If α, β ∈ R are such that 1-2 i (here i ^{2}=-1 ) is a root of z^{2}+α z+β=0, then (α-β) is

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4-1.Complex numbers

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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 ..... .

A

$-3$

B

$-7$

C

$7$

D

$3$

(JEE MAIN-2021)

Solution

$\because \alpha, \beta \in R \Rightarrow$ other root is $1+2 i$

$\alpha=-($ sum of roots $)=-(1-2 i+1+2 i)=-2$

$\beta=$ product of roots $=(1-2 i)(1+2 i)=5$

$\therefore \alpha-\beta=-7$

Standard 11

Mathematics

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