Find the values of k for which the following equation has equal roots:
9x2 + kx + 1 = 0
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Discuss the nature of the roots of the following equation without actually solving it:
3x2 - 2x + 5 = 0
x2 - 2kx + 7k - 12 = 0
(3k + 1)x2 + 2(k + 1)x + k = 0