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JEE Main 202125 FebruaryEvening Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Evening Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2021 · 25 February · Evening Shift · Mathematics · Quadratic Equation

If α, β ∈ R are such that 1 - 2i (here i ^ 2 = - 1 ) is a root of z...

If α,β∈R\alpha, \beta \in R are such that 1−2i1 - 2i (here i2=−1{i}^{2} = - 1) is a root of z2+\alphaz+β=0{z}^{2} + \alphaz + \beta = 0, then (α−β)\left(\alpha - \beta\right) is equal to:

Options

  1. A−7- 7
  2. B77
  3. C−3- 3
  4. D33

Correct answer

A. −7- 7

Step-by-step solution

∵ \alpha, \beta \in R ⇒otherrootisother root is1 + 2i</p><p></p><p>\alpha = -(sumofroots)( sum of roots )= - \left(1 - 2i + 1 + 2i\right) = - 2</p><p></p><p>\beta =productofrootsproduct of roots= \left(1 - 2i\right)\left(1 + 2i\right) = 5</p><p></p><p>∴ \alpha - \beta = - 7</p><p>option(1)</p><p>option \left(1\right)

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