If both the roots of the quadratic equation x 2 - m x + 4 = 0 are real and distinct and they lie in the interval 1 , 5 , then m lies in the interval: Note: In the actual JEE paper interval was 1 , 5

Step-by-step solution

Given roots of x 2 - m x + 4 = 0 are distinct and lies in 1 ,   5 , Following conditions must be true ( i ) D > 0 ⇒ m 2 - 16 > 0 ⇒ m - 4 m + 4 > 0 ⇒ m ∈ - ∞ ,   - 4 ∪ 4 ,   ∞ ( i i ) f 1 > 0 ⇒ m < 5 ( i i i ) f 5 > 0 ⇒ m < 29 5   ( i v ) 1 < - b 2 a < 5 ⇒ 2 < m < 10 Taking intersection of all conditions, we get m ∈ 4 ,   5