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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2012 · Mathematics · Quadratic Equation

If α and β are the roots of the equation x^2-q(1+x)-r=0 , then what...

If α\alpha and β\beta are the roots of the equation x2−q(1+x)−r=0x^2-q(1+x)-r=0, then what is (1+α)(1+β)(1+\alpha)(1+\beta) equal to?

Options

  1. A1−r1-r
  2. Bq−rq-r
  3. C1+r1+r
  4. Dq+rq+r

Correct answer

A. 1−r1-r

Step-by-step solution

x2−qx+(−q−r)=0α+β=qαβ=−q−r(1+α)(1+β)1+α+β+αβ1+q−q−r1−r.\begin{gathered}x^2-q x+(-q-r)=0 \\ \alpha+\beta=q \\ \alpha \beta=-q-r \\ (1+\alpha)(1+\beta) \\ 1+\alpha+\beta+\alpha \beta \\ 1+q-q-r \\ 1-r.\end{gathered}
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