Question

Statement-1: f(x) = x² + x + 1/x² + 2x + 5 > 0 ∀x∈R

Statement-2: ax² + bx + c > 0 ∀x∈R if a > 0 and b² – 4ac < 0.

(A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1.

(C) Statement – 1 is True, Statement – 2 is False. 

(D) Statement – 1 is False, Statement – 2 is True

Answer 1

 Correct option (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. 

Explanation:

ax² + bx + c = 0 Put x = 1 a + b + c = 0 which is given So clearly ‘1’ is the root of the equation Nothing can be said about the sign of the roots. ‘c’ is correct.