The integral value of a , for which the quadratic expression a x 2 + a - 2 x - 2 is negative for exactly two integral values of x, is

Step-by-step solution

Let, f x = a x 2 + a - 2 x - 2 ∴ f 0 = - 2 and f - 1 = 0 Since, the quadratic expression is negative for exactly two integral values ⇒ f 1 < 0 and f 2 ≥ 0 ⇒ a + a - 2 - 2 < 0 and 4 a + 2 a - 4 - 2 ≥ 0 ⇒ a < 2 and a ≥ 1 ⇒ a ∈ 1 , 2 Hence, the integral value of a = 1