WolframAlpha is solving for all five variables at once. The roots in radicals that it gives are when A = 0 (in which case, you have a quartic, which are solvable in radicals).
Aaron Meurer On Wed, Jan 20, 2016 at 10:05 AM, Denis Akhiyarov <[email protected] > wrote: > Oscar, you need to click on "more roots" in wolfram alpha to see the > algebraic solution, which is definitely confusing. > > On Wednesday, January 20, 2016 at 3:55:37 AM UTC-6, Oscar wrote: > >> On 20 January 2016 at 05:46, Denis Akhiyarov <[email protected]> >> wrote: >> > On Tuesday, January 19, 2016 at 11:41:47 PM UTC-6, Denis Akhiyarov >> wrote: >> >> >> >> no algebraic roots according to this theorem: >> >> https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem >> >> The theorem only shows that a general algebraic solution for *all* >> quintics (or higher degree polynomials) is not possible. In this case >> it is not a fully general quintic since the coefficients of x^3 and >> x^2 are both zero. I'm not sure how to check based on the coefficients >> of a polynomial whether or not its Galois group is solvable. Can sympy >> do that? >> >> To the OP: do you need to solve this in terms of symbols A, B etc. or >> is it acceptable to solve it using particular numbers for the >> coefficients? You may have better luck using the actual numbers. >> >> > actually this case looks like has some special properties and hence has >> some >> > roots according to Wolfram: >> > >> > http://www.wolframalpha.com/input/?i=A*x%5E5%2BB*x%5E4%2BC*x-D%3D0 >> >> My interpretation of that Wolfram output is that Wolfram is unable to >> solve this quintic (or rather this general family of quintics). >> >> -- >> Oscar >> > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/b8e597b0-990e-4f5a-b2ee-0dce9889c816%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/b8e597b0-990e-4f5a-b2ee-0dce9889c816%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6J%2BFEPhT%2BH3A9tY3L8r-_k1fteKkm%3Dp2JU45JVCTcOKQQ%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
