Discrimant and matrices

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In summary, there is a general formula for rewriting the quadratic, cubic, and quartic determinant in terms of matrices and matrix operations such as trace and determinant. The formula can be found in the Wikipedia article on discriminants of polynomials, which also provides the specific formula for n=4. However, there are also resources available on the internet for specific values of n.
  • #1
Jhenrique
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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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  • #2
The answer is in the very wiki article that you cite.
 
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  • #3
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.
 
  • #4
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?
 
  • #5
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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1. What is the definition of a discriminant in mathematics?

A discriminant in mathematics refers to a number that is calculated from the coefficients of a quadratic equation. It is used to determine the nature of the solutions to the equation, whether they are real, complex, or repeated.

2. How is the discriminant used to find the number of solutions to a quadratic equation?

The value of the discriminant is used to determine the number of solutions to a quadratic equation. If the discriminant is positive, the equation has two distinct real solutions. If it is zero, the equation has one real solution. And if it is negative, the equation has no real solutions.

3. How do you calculate the discriminant of a quadratic equation?

The discriminant of a quadratic equation is calculated using the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation in the form ax^2 + bx + c. This formula is derived from the quadratic formula, which is used to solve quadratic equations.

4. What is the relationship between the discriminant and the graph of a quadratic equation?

The discriminant is related to the graph of a quadratic equation in that it can be used to determine the type of graph the equation will produce. If the discriminant is positive, the graph will have two x-intercepts. If it is zero, the graph will have one x-intercept. And if it is negative, the graph will not intersect the x-axis at all.

5. How are matrices used in solving systems of equations?

Matrices are used in solving systems of equations by representing the coefficients and constants of the equations in a structured format. This allows for efficient manipulation and solving of the equations using various matrix operations such as row reduction and finding inverses.

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