Cubic resolvent of a quartic
= Cubic resolvent of a quartic
= Resolvent cubic
{synonym}
For a depressed quartic $x^4+px^2+qx+r$ with roots $\alpha_1,\ldots,\alpha_4$, the three pair-partition quantities $\alpha_1\alpha_2+\alpha_3\alpha_4$ and its two analogues are the roots of
$$
y^3-py^2-4ry+(4pr-q^2).
$$
The Galois action on these roots is the quotient of its action on the four quartic roots by the <Klein four-group>.