Question

If, (a + 1)x^2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have equal roots?

(a) (-∞, -1)

(b) [-1, ∞)

(c) (0, 1)

(d) Not possible

I got this question in an international level competition.

This key question is from Applications of Quadratic Equations in portion Complex Numbers and Quadratic Equations of Mathematics – Class 11

Answer 1

The correct option is (d) Not possible

Explanation: For, equal 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

So, from here it is clear that a = -1 is not possible because the equation is becoming linear.