**Correct option (c) (5, 24) **

**Explanation:**

D ≥ 0

(–2a)2– 4(a – 5) (a – 4) ≥ 0

*⇒ *9a –20 ≥ 0

a ≥ 20/9 .......(1)

(a –5) ƒ(1) < 0

(a –5) (a–5 –2a + a – 4) < 0

(a –5) (–a) < 0

a > 5 ........(2)

(a –5) ƒ(2) < 0

(a –5) (4(a – 5) – 4a + a – 4) < 0

*⇒ *(a – 5) (a – 24) < 0

*⇒ *5 < a < 24 .........(3)

From (1), (2), and (3) a ∈ (5,24)