Question

Statement-1 : The number of real roots of |x|² + |x| + 2 = 0 is zero.

Statement-2 : ∀x∈R, |x| ≥ 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:

quation can be written as (2^x)² – (a – 4) 2^x – (a – 4) = 0

⇒ 2x = 1 & 2^x = a – 4 Since x ≤ 0 and 2x = a – 4 [∵ x is non positive]

∴ 0 < a – 4 ≤ 1 

⇒ 4 < a ≤ 5 i.e., a∈ (4, 5]