The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is
Correct Answer :
3
Solution :
Correct Option: C
x2 + (a + 3) x – (a+5) = 0
α2 + β2 = (α + β)2 – 2 αβ = (-(a + 3))2 – 2(– (a + 5))
= a2 + 9 + 6a + 2 (a + 5)
= a2 + 8a + 19
= (a + 4)2 + 3
The minimum value is 3, at a = –4. Choice (3)
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