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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 |
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Answer» 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 (2x)2 – (a – 4) 2x – (a – 4) = 0 ⇒ 2x = 1 & 2x = 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] |
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