1,1

Matthew Moore, Theorems and Algorithms Associated with Solving the General Quintic [Appears to give incorrect formula for the Brioschi quintic]

Eric Weisstein's World of Mathematics, Brioschi Quintic Form

The discriminant is 5^5*n^8*(-1+1728n)^2. - Klaus Brockhaus.

Discriminant[p_?PolynomialQ, x_] := With[{n = Exponent[p, x], k = Exponent[D[p, x], x]}, Cancel[((-1)^(n(n - 1)/2)Resultant[ p, D[p, x], x]) Coefficient[p, x, n]^(n - k - 2)]] ; Table[Discriminant[x^5 - 10p x^3 + 45p^2 x - p^2, x], {p, 1, 20}]

Cf. A134450.

Sequence in context: A015398 A034614 A140501 this_sequence A048053 A130429 A130430

Adjacent sequences: A134445 A134446 A134447 this_sequence A134449 A134450 A134451

nonn

Artur Jasinski (grafix(AT)csl.pl), Oct 26 2007, Oct 28 2007

Corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 28 2007