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Math Help - Finding polynomial func. with given zeros

  1. #1
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    Unhappy 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.
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  2. #2
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    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.
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  3. #3
    MHF Contributor

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    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 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 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.
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