If x^2 + k (4x + k – 1) + 2 = 0 has equal roots, then k = A. (-2)/3, 1 B. 2/3, (- 1) C. 3/2, 1/3

Question

If x² + k (4x + k – 1) + 2 = 0 has equal roots, then k =

A. \(-\frac{2}{3},1\)

B. \(\frac{2}{3},-1\)

C. \(\frac{3}{2},\frac{1}{3}\)

D. \(-\frac{3}{2},-\frac{1}{3}\)

Answer 1

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