For the next two (2) items that follow:

Let α and β (α < β) be the roots of the equation xConsider the following

1. α + β + αβ > 0

2. α^{2}β + β^{2}α > 0

This question was previously asked in

NDA (Held On: 17 April 2016) Maths Previous Year paper

Option 2 : 2 only

Electric charges and coulomb's law (Basic)

41133

10 Questions
10 Marks
10 Mins

__Calculation:__

Given: x^{2} + bx + c = 0, where b > 0 and c < 0. And α & β are the roots of the equation.

For statement (1),

α + β + αβ = -b + c

⇒ α + β + αβ = c – b

We know, c < 0 & b > 0. So, c – b < 0.

⇒ α + β + αβ < 0

∴ **Statement (1) **is incorrect.

For statement (2),

α^{2}β + β^{2}α = αβ(α + β)

⇒ α^{2}β + β^{2}α = (c)(-b)

⇒ α^{2}β + β^{2}α = -bc

We know, c < 0 & b > 0. So, -bc > 0.

⇒ α^{2}β + β^{2}α > 0

∴ **Statement (2)** is correct.