In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: In each case:
* The coefficients of the resolvent cubic can be obtained from the coefficients of P(x) using only sums, subtractions and multiplications.
* Knowing the roots of the resolvent cubic of P(x) is useful for finding the roots of P(x) itself. Hence the name “resolvent cubic”.
* The polynomial P(x) has a multiple root if and only if its resolvent cubic has a multiple root.
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| - Cúbica resolvente (es)
- Resolvent cubic (en)
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| - En álgebra, una ecuación cúbica resolvente es uno de varios polinomios cúbicos distintos, aunque relacionados, definidos a partir de un polinomio mónico de grado cuatro: En cada caso:
* Los coeficientes de la cúbica resolvente se pueden obtener a partir de los coeficientes de utilizando solo sumas, restas y multiplicaciones.
* Conocer las raíces de la cúbica resolvente de es útil para encontrar las propias raíces de . De ahí el nombre de "cúbica resolvente".
* El polinomio tiene una raíz múltiple si y solo si su cúbica resolvente tiene una raíz múltiple. (es)
- In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: In each case:
* The coefficients of the resolvent cubic can be obtained from the coefficients of P(x) using only sums, subtractions and multiplications.
* Knowing the roots of the resolvent cubic of P(x) is useful for finding the roots of P(x) itself. Hence the name “resolvent cubic”.
* The polynomial P(x) has a multiple root if and only if its resolvent cubic has a multiple root. (en)
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| - En álgebra, una ecuación cúbica resolvente es uno de varios polinomios cúbicos distintos, aunque relacionados, definidos a partir de un polinomio mónico de grado cuatro: En cada caso:
* Los coeficientes de la cúbica resolvente se pueden obtener a partir de los coeficientes de utilizando solo sumas, restas y multiplicaciones.
* Conocer las raíces de la cúbica resolvente de es útil para encontrar las propias raíces de . De ahí el nombre de "cúbica resolvente".
* El polinomio tiene una raíz múltiple si y solo si su cúbica resolvente tiene una raíz múltiple. (es)
- In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: In each case:
* The coefficients of the resolvent cubic can be obtained from the coefficients of P(x) using only sums, subtractions and multiplications.
* Knowing the roots of the resolvent cubic of P(x) is useful for finding the roots of P(x) itself. Hence the name “resolvent cubic”.
* The polynomial P(x) has a multiple root if and only if its resolvent cubic has a multiple root. (en)
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