The value of α 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

1

0

3

2
A.
1
x^{2} – (a – 2)x – a – 1 = 0
⇒ α + β = a – 2
α β = –(a + 1)
α^{2} + β^{2} = (α + β)^{2}  2αβ
= a^{2} – 2a + 6 = (a – 1)^{2} + 5
⇒ a = 1