Marty Green
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 Apr 15 awarded Popular Question 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 $\mathbb Q$