The minimum possible value of the sum of the squares of the roots

• Quant Quadratic

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

1. 1
2. 2
3. 3
4. 4

Answer

x² + (a + 3)x - (a + 5) = 0

α² + β² = (α + β)² – 2αβ

= (-(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.

The correct option is C.