# Finding polynomial func. with given zeros

• Sep 7th 2009, 01:07 PM
FaRmBoX
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.
• Sep 7th 2009, 01:31 PM
FaRmBoX
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.
• Sep 7th 2009, 05:43 PM
HallsofIvy
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 $\displaystyle 1+ \sqrt{3}i= 1+ i\sqrt{3}$ (that is, the "i" is outside the square root). In that case, in order to have integer coefficients you must also have $\displaystyle 1- i\sqrt{3}$ 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.