Any quadratic equation in the form ax² + bx + c = 0 has equal roots if and only if Discriminant, D = 0

Where, D = b² – 4ac

In the given equation,

a = 2

b = k

c = 3

Now, above equation will have equal roots if

D = 0

i.e.

(k)² – 4(2)(3) = 0

⇒ k² = 24

⇒ k= ±2√6