Exact formula of the roots of a polynomial

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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.

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