If one root of the equation x² - kx + k = 0 exceeds the other by 2√3, then which one of the following is a value of k?

Let roots be α and β with α - β = 2√3. Then α + β = k and αβ = k. Also (α - β)² = (α + β)² - 4αβ, so 12 = k² - 4k, i.e., k² - 4k - 12 = 0, giving k = 6 or k = -2. Among the options, k = 6 is valid.