Can Discriminants of Polynomial Equations Be Expressed Using Matrix Operations?

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Discussions focus on whether the discriminants of quadratic, cubic, and quartic polynomial equations can be expressed using matrix operations. Participants confirm that the relevant formulas are available in the cited Wikipedia article, which outlines the complex relationships. There is a request for specific matrix formulas that replace coefficients for these discriminants. The article provides general formulas, and users are encouraged to apply them for specific cases. The conversation emphasizes the connection between polynomial discriminants and matrix operations.
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Is possible to rewrite the quadratic, cubic and quartic determinant in terms of matrices and matrix operations (trace and determinant)?

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https://en.wikipedia.org/wiki/Discriminant_of_a_polynomial#Formulas_for_low_degrees
 
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The answer is in the very wiki article that you cite.
 
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micromass said:
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.
 
micromass said:
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?
 
Jhenrique said:
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##.
 
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