Complex zeros of polynomial functions with real coefficients come in conjugate pairs. That means that if is a zero of a given polynomial function, then must also be a zero of that same polynomial function.
The conjugate of is and the conjugate of is . Now we know that we have at least 4 zeroes, so the minimum degree polynomial function is 4th degree.
If is a zero of the polynomial function , then is a factor of .
All you need to do is multiply the factors to obtain a general form representation of your polynomial.
My calculator said it, I believe it, that settles it