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March 5th, 2009, 03:05 AM   #1
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Finding Roots of a Polynomial Using Galois Theory....

Hi guys,

I need to find all the complex roots of X^4 - Sqrt(6) + 7/4 using Galois Theory.

I have books containing all the theory but can not find a worked example to see how this theory is applied.

Any help on how to answer this question would be greatly appreciated!

Thanks in advance.
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March 5th, 2009, 01:49 PM   #2
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Re: Finding Roots of a Polynomial Using Galois Theory....

Galois theory is only needed for quintics and above.



The second factor has the two imaginary roots

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March 5th, 2009, 03:55 PM   #3
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Re: Finding Roots of a Polynomial Using Galois Theory....

Oh....ok, thanks aswoods- well the question says using Galois Theory. :-s

The second part says, also using Galois Theory, find all the complex roots of X^4+1/2X^2-2X+7/4 & calculate the Galois Group of the quartic X^4-2X^2+4X-2.

Any ideas?

Thanks.
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March 8th, 2009, 07:57 AM   #4
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Re: Finding Roots of a Polynomial Using Galois Theory....

hi! i jst want to know which is the biggest slope between -7 and 7
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