Is possible to rewrite the quadratic, cubic and quartic determinant in terms of matrices and matrix operations (trace and determinant)? https://en.wikipedia.org/wiki/Discriminant_of_a_polynomial#Formulas_for_low_degrees
But exist in somewhere in the internet the matrix formula (already replaced by coefficients) for the quadratic, cubic and quartic discriminant?
Yes, of course. The wiki link gives the general formula. So just take a specific ##n##. It also gives the formula for ##n=4##.