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What is the value of k for which the sum of the squares of the roots of 2 x^2-2(k-2) x-(k+1)=0 is minimum?

Options

  1. A-1
  2. B1
  3. C3 2
  4. D2

Correct answer

C. 3 2

Step-by-step solution

For 2 x^2-2(k-2) x-(k+1)=0 Let roots be and . aligned & + =k-2 ; =- k+1 2 & ^2+ ^2=( + )^2-2 & ^2+ ^2=(k-2)^2+(k+1) & ^2+ ^2=k^2-4 k+4+k+1 & ^2+ ^2=k^2-3 k+5 & ^2+ ^2= (k- 3 2 )^2+ (5- 9 4 ) aligned for minimum value k= 3 2

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