Question
Quantitative Aptitude Question on Maxima and Minima
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
3
Explanation
Solution
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.