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

NDA 2019 Mathematics question

What is the value of k for which the sum of the squares of the roots of is minimum?

Answer: (C)

and . 2)^2$+(k+1)

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Question ID VK-029056