I'm looking for a closed formula given one (or all) root of a polynomial $P=aX^4 +bX^3+cX^2+dX+e$.

I'm not interested in the efficiency of such a formula. On the contrary, I would like to show my students that this formula is very complicated.

  • $\begingroup$ You can search for the Cardano's formula. $\endgroup$ May 6, 2019 at 17:14
  • $\begingroup$ And solving the quartic equation $\endgroup$ May 6, 2019 at 17:15
  • $\begingroup$ @PeterForeman That's it, thanks ! You can make it an answer if you wish (what about also copying the image here instead of juste pointing to the webpage)? $\endgroup$
    – Colas
    May 6, 2019 at 17:19

1 Answer 1


The quartic formula is below which should also work for the cubic case. enter image description here


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