You can put this solution on YOUR website! By Vieta's formulas, the sum of the roots is real, so the sum of the other roots must be C - 6i for real C. There are actually infinitely many polynomials satisfying this.
We know the polynomial must be in the form
where Q(x) is a polynomial with complex coefficients. If we let two roots of Q(x) be -5i and -i, then the polynomial will have real coefficients. Therefore we can let where R(x) has real coefficients.
where R(x) is a polynomial with real coefficients. I'm sure many other solutions exist, but the problem only asks for one polynomial.
