Equation x² + k (4x + k – 1) + 2 = 0 has equal roots

d = 0

d = b² – 4ac = 0

Here a = 1, b = 4k, c = k² – k + 2

⇒ 16 k² – 4(k² – k + 2) = 0

⇒ 12 k² + 4k – 8 = 0

⇒ 3k² + k – 2 = 0

⇒ (3k – 2) (k + 1) = 0

⇒ K = 2/3, – 1