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 Yearling
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Jan
2
comment Is there a simple explanation why degree 5 polynomials (and up) are unsolvable?
No I don't think it does. I'm in much more traditional territory. The Arnold proof comes from a totally novel perspective.
Jan
2
comment Is there a simple explanation why degree 5 polynomials (and up) are unsolvable?
Yes, that's right. By the way, for me it makes things a little simpler if I let all my polynomials be monic (leading coefficient A=1) so I can just think: the product of the roots is the constant coefficient, and the sum of the roots is the (negative) coefficient in x. Anyhow, you see how the coefficients of the polynomial are the ELEMENTARY symmetric functions of the roots, and the derived functions (my p's and q's) are (general) symmetric functions. Which can always be worked out from the elementary functions.
Jan
1
comment Is there a simple explanation why degree 5 polynomials (and up) are unsolvable?
You should check out some of my blogposts which I linked above. But to your specific question about the formulas for the p's and q's, do you understand how any function symmetric in the roots can be easily found from the elementary symmetric functions which are the coefficcients of the polynomial? So for a quadratic equation where the roots are a and b, you can easily look at the equation and tell what is a^2 + b^2?
Jul
26
revised Given $\tan A + \tan B = 3x$ and $\tan A \tan B = 2x^2$, find $\tan A - \tan B$
follow-up question on different method of solving
Jul
26
suggested approved edit on Given $\tan A + \tan B = 3x$ and $\tan A \tan B = 2x^2$, find $\tan A - \tan B$
May
13
awarded  Yearling
May
6
awarded  Nice Question
Dec
8
awarded  Caucus
Nov
12
awarded  Enlightened
Nov
12
awarded  Nice Answer
Oct
11
answered In high school statistics, why does it seem like equations come out of the sky
Jul
30
answered Roots for quintic equations
Jul
11
awarded  Enlightened
Jul
11
awarded  Nice Answer
Jul
2
awarded  Curious
Jun
6
accepted Resolvent of the Quintic…Functions of the roots
Jun
6
revised Intuitive reasoning why are quintics unsolvable
point to follow-up discussion
May
13
awarded  Yearling
Apr
30
answered Galois group of $x^3 - 2 $ over $\mathbb Q$
Feb
19
awarded  Nice Question