Question

The all possible values of a for which one root of the equation (a – 5)x² – 2ax + a – 4 = 0 is smaller than 1 and the other greater than 2 is 

(a)  [5, 24) 

(b)  (5, 24] 

(c)  (5, 24) 

(d)   none of these 

Answer 1

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)