Question

x^2 +4kx + k^2 - k +2 = 0 has real and equal roots what is the value of k ?​

Answer 1

Answer:

Given quadratic equation is

:  x2 + 4kx + (k2 – k + 2) = 0

 For equal roots, we have

 b2 – 4 ac = 0

 ⇒ (4k)2 – 4(1) (k2 - k + 2) = 0 

⇒ 16k2 – 4k2 + 4k – 8 = 0 

⇒ 12k2 + 4k – 8 = 0  or 3k2 + k – 2 = 0 

⇒ 3k2 + 3k – 2k - 2 = 0 

⇒ 3k(k + 1) – 2(k + 1) = 0 

⇒ (k + 1)(3k – 2) = 0 

⇒ k + 1 = 0 or 3k – 2 = 0  k = – 1 or k = -1or k=2/3