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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Quadratic Equation

BITSAT 2021 · Mathematics · Quadratic Equation

Find the value of a such that the sum of the squares of the roots...

Find the value of aa such that 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 is least.

Options

  1. A4
  2. B2
  3. C1
  4. D3

Correct answer

C. 1

Step-by-step solution

Let α,β\alpha, \beta be the roots of the equation. ∴α+β=a−2\therefore \alpha+\beta=a-2 and αβ=−(a+1)\alpha \beta=-(a+1) Now, α2+β2=(α+β)2−2αβ=(a−2)2+2(a+1)=(a−1)2+5∴α2+β2\alpha^{2}+\beta^{2}=(\alpha+\beta)^{2}-2 \alpha \beta=(a-2)^{2}+2(a+1)=(a-1)^{2}+5\therefore \alpha^{2}+\beta^{2} will be minimum if (a−1)2=0(a-1)^{2}=0, i.e. a=1a=1.
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