Find the values of k for each of the following quadratic equations, so that they have two equal roots. (i) 2x² + kx + 3 = 0 (ii) kx(x - 2) + 6 = 0

i) If 2x² + kx + 3 = 0 has equal roots, then b² - 4ac = 0. Here, a = 2, b = k, c = 3
2x² + kx + 3 = 0
b² - 4ac = 0
k² - 4(2)(3) = 0
k² = 24
k = ±√24 = ±2√6
ii) If kx² - 2kx + 6 = 0 has equal roots, then b² - 4ac = 0. Here, a = k, b = -2k, c = 6
kx(x - 2) + 6 = 0
kx² - 2kx + 6 = 0
(-2k)² - 4(k)(6) = 0
4k² - 24k = 0
4k(k - 6) = 0
For k = 0, the equation is not quadratic.
k = 6