Key points are not available for this paper at this time.
to Cardanos formulas for the general cubic and quartic polynomials (cf. 1, Section 14.7, for example) and to determine the precise Galois group. In particular, the roots are produced in an order which is a cyclic permutation of the roots (see the Remark before the examples below), which can be useful in other computations (e.g. cf. 3). We work over the rationals Q , but the results are valid over any field K of characteristic different from 2 and 5. Let x 1 ,x 2 ,x 3 ,x 4 ,x 5 be the roots of the general quintic polynomial x 5 - s 1 x 4 + s 2 x 3 - s 3 x 2 + s 4 x - s 5 where the s i are the eleme
David S. Dummit (Sun,) studied this question.