Explanation

For the quadratic equation 3x^2 - 6x + k = 0 to have equal roots, the discriminant b^2 - 4ac must be 0.

Here, a = 3, b = -6, and c = k.

Setting the discriminant to 0 gives (-6)^2 - 4(3)(k) = 0.

Solving this, 36 - 12k = 0, which yields k = 3.