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

Question

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, 0 , ∞, 0,1, 0,3 - 2 2, 3 - 2 2 , 1

MARKS App · Accepted Answer

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

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