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Statement-1: One is always one root of the equation (l – m)x2 + (m – n) x + (n – l ) = 0, where l, m, n∈R.Statement-2: If a + b + c = 0 in the equation ax2 + bx + c = 0, then 1 is the one root.(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: The roots of the given equation will be of opposite signs. If they are real and their product is negative D ≥ 0 and product of root is < 0 ⇒ (a3 – 8a – 1)2 – 8(a2 – 4a) ≥ 0 and a2 - 4a/2 < 0 ⇒ a2 – 4a < 0 ⇒ 0 < a < 4. |
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