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Math Help - Quickest method of finding roots....

  1. #1
    AAM
    AAM is offline
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    Quickest method of finding roots....

    Hi guys,

    What is the quickest way to find the 4 complex roots of X^4+2=0 ?

    I'm trying to find the splitting field for this equation over Q.

    Many thanks in advance. :-) x
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  2. #2
    MHF Contributor

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    Quote Originally Posted by AAM View Post
    Hi guys,

    What is the quickest way to find the 4 complex roots of X^4+2=0 ?

    I'm trying to find the splitting field for this equation over Q.

    Many thanks in advance. :-) x
    x^4= -2. Write -2 in polar form- -2= 2 (cos(\pi)+ i sin(\pi)) and use DeMoivre's formula.
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  3. #3
    MHF Contributor

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    you can also write: 0=x^4+ 2 = (x^2 + \sqrt{2})^2 - 2\sqrt{2} x^2=(x^2 + \sqrt[4]{8} x + \sqrt{2})(x^2 - \sqrt[4]{8} x + \sqrt{2}).
    Last edited by NonCommAlg; May 18th 2009 at 10:37 PM.
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