(63)

Sol. case- I: Both roots are greater than 2.

or one root is 2 & other is greater than 2

D 0

⇒ (a – 3) 2 – 4a 0

⇒ a 2 – 10 a + 9 0

(a – 1) (a – 9) 0

a ∈ (– ∞ , 1] ∪ [9, ∞ ) ... (i)

⇒ > 2

⇒ a > 7 ... (ii)

f(2) 0 ⇒ 4 – 2(a – 3) + a 0

– a + 10 0 ⇒ a 10... (iii)

(i) ∩ (ii) ∩ (iii) gives is

a ∈ [9, 10] ... (iv)

Case-II: One root is greater than 2

f(2) < 0 ⇒ – a + 10 < 0

⇒ a > 10 ⇒ a ∈ (10, ∞ )....(v)

(iv) ∪ (v) gives final answer as

a ∈ [9, ∞ )

Least value of 7a is 63.

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