We will use the The Conjugate Zeros Theorem: If P(x) is a polynomial with real coefficients, and if a + bi is a zero of P , then a - bi is a zero of P.

Since 3i is one zero then -3i is also a zero.

Now we can write the polynomial:

(x - 6)^2(x - 3i)(x - (-3i)) = (x^2 - 12x + 36)(x^2 + 9) = x^4 - 12x^3 + 45x^2 - 108x + 324

The zeros of the polynomial f(x) = x^4 - 12x^3 + 45x^2 - 108x + 324 are 6 with multiplicity 1, 3i and -3i.