This question tests the concept of discriminant. From the textbook, a quadratic equation ax² + bx + c = 0 has two equal roots when the discriminant b² - 4ac = 0. For part (i), substituting a=2, b=k, c=3 gives k² = 24. For part (ii), after expanding to standard form kx² - 2kx + 6 = 0, we apply the discriminant condition. Note that k=0 is rejected as it would not form a quadratic equation.