The value of k for which both the roots of the equation 4 x 2 - 20 k x + 25 k 2 + 15 k - 66 = 0 are less than 2 , lies in

Step-by-step solution

Let, f x = 4 x 2 - 20 k x + 25 k 2 + 15 k - 66 = 0 … … … … … . . ( i ) Let the roots of f x = 0   b e   α ,   β Since α ,   β are real. ∴   ∆ ≥ 0 ⇒ 400 k 2 - 4.4 25 k 2 + 15 k - 66 ≥ 0 ⇒   - 15 k + 66 ≥ 0         ⇒         k ≤ 22 5 … … … … . . i i We have α ,   β < 2 ∴     α + &#94