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JEE Mains · Maths · STD 11 - 4.1 complex nubers
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 \(3\)
Answer & Solution
Correct Answer
(B) \(-7\)
Step-by-step Solution
Detailed explanation
\(\because \alpha, \beta \in R \Rightarrow\) other root is \(1+2 i\) \(\alpha=-(\) sum of roots \()=-(1-2 i+1+2 i)=-2\) \(\beta=\) product of roots \(=(1-2 i)(1+2 i)=5\) \(\therefore \alpha-\beta=-7\)
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