JEE Mains 2020 Model Paper 1 New Pattern

x2−8kx+16(k2−k+1) = 0
Since roots are real and distinct, D > 0
⇒ 64k2−64(k2−k+1) > 0 ... (1)
⇒ k > 1
Also, from the figure, we have
−

b

2a

> 4 ⇒

8k

2

> 4
⇒ k > 1 ... (2)
Further
f (4) ≥ 0
⇒ 16 - 32k + 16 (k2 - k + 1) ≥ 0
⇒ k2 - 3k + 2 ≥ 0
⇒ k ≤ 1 or k ≥ 2 ... (3)
From (1), (2) and (3)
K min = 2