Pre-calculus answer an explanation needed

Question

Use the partial solution sets to recreate the functions.

x={3,−1,3i,−√3}

x={−1,2,−5,5+√6/4}

Need help with the two problems. Also an easiest explanation possible because it is hard for me to start figuring out the steps.

Answer 1

If f(x) is a polynomial function with integer coefficients and if 3, -1, 3i, and -√3 are roots, then -3i and √3 must also be roots.

A possible function is f(x) = (x-3)(x+1)(x-3i)(x+3i)(x-√3)(x+√3) = (x²-2x-3)(x²+9)(x²-3)