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BITSAT2021MathematicsQuadratic EquationActual

Find the value of a such that the sum of the squares of the roots of the equation x²-(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 , be the roots of the equation. + =a-2 and =-(a+1) Now, ²+ ²=( + )²-2 =(a-2)²+2(a+1)=(a-1)²+5 ²+ ² will be minimum if (a-1)²=0 , i.e. a=1 .

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