Question

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The Correct Option is C

The correct answer is (C):
x 2 + (a + 3) x – (a+5) = 0
α 2 + 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.