The minimum possible value of the sum of the squares of the roots of the equation x^2 + (a + 3)x – (a + 5) = 0 is

A) 1

B) 2

C) 3

D) 4

Option (C)

From CAT 2017 – Quantitative Aptitude – Algebra – Quadratic Equations, we can see that,

b and c can be the roots of the given equation.

We have to find, b^2 + c^2 = (b+c)^2 â€“ 2bc

b+c = -(a+3) and bc = -(a+5)

b^2 + c^2 = (a+3)^2 + 2(a+5) = a^2 + 8a + 19

Min value of a quadratic equation = -Discriminant (D)/4*First term

D = b^2 â€“ 4ac = 64 â€“ 76 = -12

Min value = 12/4 = 3

Option (C)

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