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March 26th, 2014, 08:34 PM   #1
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Solution for algebraic equations

I noticed that it's always possible to find the roots of polynomials of kind:





So I thought to transform the quadratic, the cubic, the quartic and the quintic function in the forms above, look:











So, comparing the equations:



implies that:


So,






Happens that


1) Is this idea correct?
2) If yes, is it possible to solve equations of the 5th, 6th, 7th... degree with this process?
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March 29th, 2014, 11:46 AM   #2
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I haven't looked at it closely for errors, seems almost obvious that this is false. I'll just directly check your final result for



Let's compute . This is



If 0, and this case is outright ruled out. Otherwise, in which case



And this is clearly not a zero of the polynomial given!
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