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 least is

Question

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 least is, 1, 3 2, 2, 5 2

MARKS App · Accepted Answer

α + β = k - 2 α β = - k + 1 2 α 2 + β 2 = α + β 2 - 2 α β = k - 2 2 + k + 1 = k 2 - 4 k + 4 + k + 1 = k 2 - 3 k + 5 ⇒ α 2 + β 2 = k - 3 2 2 + 11 4 Which is least for k = 3 2

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