Find the values of k so that the quadratic equation 3x² - 2kx + 12 = 0 has equal roots.

The given quadratic equation is 3x² - 2kx + 12 = 0
On comparing it with the general quadratic equation ax² + bx + c = 0, we obtain
a = 3, b = -2k and c = 12
Discriminant, 'D' of the given quadratic equation is given by
D = b² - 4ac = (-2k)² - 4 × 3 × 12 = 4k² - 144
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
⇒ 4k² - 144 = 0
⇒ 4(k² - 36) = 0
⇒ k² = 36
⇒ k = ±6
Therefore, the values of k for which the quadratic equation 3x² - 2kx + 12 = 0 will have equal roots are 6 and -6.