The number of integral values of a for which the inequality 3 - x - a > x 2 is satisfied by atleast one negative x, must be equal to

Step-by-step solution

Given inequality is 3 - x - a > x 2           . . . 1 ⇒   x - a < 3 - x 2 or - 3 + x 2 < x - a < 3 - x 2 or x 2 - x + a - 3 < 0           2 and x 2 + x - a + 3 < 0         . . . 3 If α , β  α < β be the real and unequal roots of the corresponding equation of Eq. 1 for all x ∈ α , β . Since Eq. 1 will have at least one negative solution. The corresponding equation of 2