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4-1.Complex numbers
medium
જો $\alpha, \beta \in R$ એવા હોય કે જેથી $1-2 i$ (અહીં $i ^{2}=-1$) એ $z^{2}+\alpha z+\beta=0$ નું બીજ હોય, તો $(\alpha-\beta)$ $=.....$ થાય.
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
