Can Discriminants of Polynomial Equations Be Expressed Using Matrix Operations?

[Jhenrique]

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

 

[micromass]

The answer is in the very wiki article that you cite.

 

[Jhenrique]

The answer is in the very wiki article that you cite.

It's true, sorry!

The formula is too complex that I didn't recognize at 1st vista.

 

[Jhenrique]

The answer is in the very wiki article that you cite.

But exist in somewhere in the internet the matrix formula (already replaced by coefficients) for the quadratic, cubic and quartic discriminant?

 

[micromass]

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 $n=4$.