If both the roots of the equation x 2 + a - 1 x + a = 0 are positive, then the complete solution set of real values of a is

Step-by-step solution

Both roots are positive ⇒ D > 0 ,   S > 0 ,   P > 0 Sum of the roots, S > 0 ⇒ - a - 1 > 0 ⇒ a - 1 < 0 ⇒ a < 1 Product of roots, P > 0 ⇒ a > 0 Discriminant, D > 0 ⇒ a - 1 2 - 4 a > 0 ⇒ a 2 + 1 - 6 a > 0 a 2 - 6 a + 1 > 0 ⇒ a > 3 + 2 2 or a < 3 - 2 2 Taking intersection we get a ∈ 0,3 - 2 2