The value of λ such that sum of the squares of the roots of the quadratic equation, x 2 + 3 - λ x + 2 = λ has the least value is:

Question

The value of λ such that sum of the squares of the roots of the quadratic equation, x 2 + 3 - λ x + 2 = λ has the least value is:, 2, 4 9, 15 8, 1

MARKS App · Accepted Answer

We have, x 2 + ( 3 - λ ) x + 2 = λ , have roots α & β . Then, f ( λ ) = α 2 + β 2 = α + β 2 - 2 α β = 3 - λ 2 - 2 2 - λ = λ 2 - 6 λ + 9 - 4 + 2 λ = λ 2 - 4 λ + 5 f ′ λ = 2 λ - 4 = 0 { for the minimum value of f λ } As f '' ( λ ) = 2 > 0 ⇒ λ = 2

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