2x² + kx + 3 = 0
For the quadratic equation 2x² + kx + 3 = 0 we have a = 2, b = k, c = 3.
Therefore
b² – 4ac = (k)² – 4 × 2 × 3 = k² – 24
For two equal roots, we have k² – 24 = 0
⇒ k² = 24
⇒ k = ±√24
⇒ k = ±2√6.