Thread: Finding polynomial func. with given zeros

I am completely lost with this one.

Find a polynomial function with integer coefficients that has the given zeros:
1+sqrt(3i) , 2 , 2 , -1-sqrt(2)

sqrt = square root of

I would appreciate all the help I can get. The 1+sqrt(3i) is throwing me off entirely.

I dont know if im correct or not, but these are the zeros I got from Conjugate pairs.

2, 2, 1+sqrt(3i), 1-sqrt(3i), -1-sqrt(2), and -1+sqrt(2)



After tedious calculations and multiplying, this is my end result:
x^6 - 4x^5 + 20x^3 - 33x^2 + 20x - 3ix^4 + 6ix^3 + 15ix^2 - 36ix + 12i - 4

If this is not correct, please explain on how i can solve this.

Please check the problem again. I doubt very much that one root was "1+ sqrt(3i)". While that is possible, I think it would be much too complicated for this level course. Are you sure it is not (that is, the "i" is outside the square root). In that case, in order to have integer coefficients you must also have as a root and to have a integer coefficients you must also have -1+ \sqrt{2} as you have. What you get does NOT have integer coefficients since "15i", "36i", etc. are not integers.