InterviewSolution
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InterviewSolution
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If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have real and distinct roots?(a) (-∞, ∞)(b) (-1, ∞)(c) [-1, ∞)(d) (-1, 1)This question was addressed to me by my school teacher while I was bunking the class.Question is from Applications of Quadratic Equations in chapter Complex Numbers and Quadratic Equations of Mathematics – Class 11 |
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Answer» RIGHT answer is (b) (-1, ∞) To explain: For, REAL and distinct roots, D > 0 Where, D = b^2 – 4ac In the equation, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0 D = [2(a+1)]^2 – 4 (a + 1)(a – 2) = 4a^2 + 4 + 8a – 4{a^2 – 2A + a – 2} = 4a^2 + 4 + 8a – 4a^2 + 4 a + 8 > 0 => 12a + 12 > 0 => 12a > -12 => a > -1 Therefore, a € (-1, ∞) |
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