If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have imaginary roots?(a) (-∞, -1)(b) (-1, ∞)(c) (-1, 1)(d) (-∞, ∞)This question was addressed to me in unit test.Asked question is from Applications of Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11

If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of

1.	If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have imaginary roots?(a) (-∞, -1)(b) (-1, ∞)(c) (-1, 1)(d) (-∞, ∞)This question was addressed to me in unit test.Asked question is from Applications of Quadratic Equations topic in section Complex Numbers and Quadratic Equations of Mathematics – Class 11
Answer» The correct option is (a) (-∞, -1) For explanation I would say: For, imaginary 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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