The value of a for which both the roots of the equation 1 - a 2 x 2 + 2 a x - 1 = 0 lie between 0 and 1 , will always be greater than

Step-by-step solution

Given equation is 1 - a 2 x 2 + 2 a x - 1 = 0 Its discriminant D = 4 and roots are 1 a - 1 , ⁡ 1 a + 1 Given, 0 < 1 a - 1 < 1 , ⁡ 0 < 1 a + 1 < 1 Now, 1 a - 1 > 0 ⇒ a > 1 , ⁡ 1 a - 1 < 1 ⇒ 1 a - 1 - 1 < 0 ⇒ 2 - a a - 1 < 0 ⇒ a < 1 or ⁡ a > 2 ∴ a > 2 .... (1) and 1 a + 1 > 0 ⇒ a > − 1 and 1 a + 1 < 1 ⇒ - a a + 1 < 0 ⇒ a < - 1 or ⁡ a > 0 ∴ a > 0 ... (2) From (1) and (2), a > 2