Question

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

Answer 1

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, ∞)