Correct Answer: D
Explanation:
Let f(x) = 4x2 – 20px + (25p2 + 15p – 66) = 0
…(1)
Since roots of (1) are real, its discriminant
= 400 p2 – 16 (25p2 + 15p – 66) ≥ 0
⇒ p ≤ 22/5 …(2)
Again the roots of (1) are less than 2 if
f(2) > 0 and their sum < 4.
⇒ p2 – p – 2 > 0 and p < 4/5
⇒ p > 2 or p < -1 and p < 4/5 …(3)
From (2) and (3), we get p < -1
i.e. p ∈ (-∞ , -1).