For a quadratic polynomial the polynomial discriminant appears in the quadratic formula however, I found this was not the case for cubic and quartic polynomials. The expressions used in the cubic and quartic formulae are different from the polynomial discriminants or at least they seem different to me. So is it just a coincidence that the polynomial discriminant of a quadratic polynomial appears in the quadratic formula or I have made a mistake somewhere and an alternate form of the discriminant is used in the cubic and quartic formulae. If the discriminants do exist in the cubic and quartic formulae then, is there a relation between them.
Asked
Active
Viewed 42 times
1
-
See https://math.stackexchange.com/questions/1732130/discriminant-of-the-cube-quartic for a partial answer for the cubic case. – Travis Willse Nov 20 '23 at 16:17
-
A very important fact is: the discriminant is null if and only if the polynomial (of degree $n$) has a multiple root. – Piquito Nov 20 '23 at 17:52