Find the value of

The given equation is: x² +k(2x+k −1)+2 = 0

Simplifying the equation: x² + 2kx + (k² – k + 2) = 0

Roots of an equation are given by the formula:

x = , where, D = b² – 4ac

For equal roots, D = 0

On comparing with ax² + bx + c = 0, we get:

a = 1, b = 2k , c = (k² – k + 2)

Therefore, D = 0

4k² – 4(k² – k + 2) = 0

⇒ 4k² – 4k² + 4k - 8 = 0

⇒ 4k – 8 = 0

⇒ 4k = 8

⇒ k = 2

∴ k = 2