Statement-1: The (x – p) (x – r) + λ (x – q) (x – s) = 0 wher

1.	Statement-1: The (x – p) (x – r) + λ (x – q) (x – s) = 0 where p < q < r < s has non real roots if λ > 0.Statement-2: The equation (p, q, r ∈R) βx2 + qx + r = 0 has non-real roots if q2 – 4pr < 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» Correct option (A) Explanation: x² − x + 1 = (x - 1/2)² + 3/4

Statement-1: The (x – p) (x – r) + λ (x – q) (x – s) = 0 where p < q < r < s has non real roots if λ > 0.Statement-2: The equation (p, q, r ∈R) βx2 + qx + r = 0 has non-real roots if q2 – 4pr < 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»

Correct option (A)

Explanation:

x² − x + 1

= (x - 1/2)² + 3/4

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