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 March 5th, 2009, 03:05 AM #1 Member   Joined: Dec 2008 Posts: 78 Thanks: 0 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.
 March 5th, 2009, 01:49 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Finding Roots of a Polynomial Using Galois Theory.... Galois theory is only needed for quintics and above. $\\x^4 - (\sqrt{6} -\frac 74) = 0 \\(x^2-\sqrt{\sqrt{6} -\frac 74})(x^2 + \sqrt{\sqrt{6} -\frac 74}) = 0$ The second factor has the two imaginary roots $x= \pm i \sqrt[4]{\sqrt{6} -\frac 74} \approx \pm 0.914524485\:i$
 March 5th, 2009, 03:55 PM #3 Member   Joined: Dec 2008 Posts: 78 Thanks: 0 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.
 March 8th, 2009, 07:57 AM #4 Newbie   Joined: Mar 2009 Posts: 1 Thanks: 0 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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