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JEE Main 2005
Exam
JEE Main
Year
2005
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2005 · Mathematics · Quadratic Equation

The value of α for which the sum of the squares of the roots of the...

The value of α\alpha for which the sum of the squares of the roots of the equation x2−(a−2)x−a−1=0x^2-(a-2) x-a-1=0 assume the least value is

Options

  1. A1
  2. B0
  3. C3
  4. D2

Correct answer

A. 1

Step-by-step solution

x2−(a−2)x−a−1=0⇒α+β=a−2αβ=−(a+1)α2+β2=(α+β)2−2αβ=a2−2a+6=(a−1)2+5⇒a=1.\begin{aligned} & x²-(a-2) x-a-1=0 \\ & \Rightarrow \alpha+\beta=a-2 \\ & \alpha \beta=-(a+1) \\ & \alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \\ & \quad=a²-2 a+6=(a-1)^2+5 \\ & \Rightarrow a=1 . \end{aligned}
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