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

Question

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,

MARKS App · Accepted Answer

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

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