The value of a for which the sum of the squares of the roots of the equation x^2 – (a – 2)x – a – 1 = 0 assume the least value is
The value of a for which the sum of the squares of the roots of the equation x2 – (a – 2)x – a – 1 = 0 assume the least value is
(a) 0
(b) 1
(c) 2
(d) 3.
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(b) : Let f (a) = α2 + β2 = (α + β)2 – 2αβ
= (a – 2)2 + 2(a + 1)
∴ f '(a) = 2(a – 2) + 2
For Maxima | Minima f '(a) = 0
=> 2[a – 2 + 1] = 0 => a = 1
Again f "(a) = 2,
f "(1) = 2 > 0 => at a = 1, f (a) will be least.
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