“Discriminant (Polynomial)”的概念、定义、习题解题方法及翻译-数学辞典

单词

Discriminant (Polynomial)

释义

Discriminant (Polynomial)

The Product of the Squares of the differences of the Polynomial Roots. For a Polynomial of degree ,

(1)

The discriminant of the Quadratic Equation

(2)

is usually taken as

(3)

However, using the general definition of the Polynomial Discriminant gives

(4)

where

are the Roots.

The discriminant of the Cubic Equation

(5)

is commonly defined as

(6)

where

			(7)
			(8)

However, using the general definition of the polynomial discriminant for the standard form Cubic Equation

(9)

gives

(10)

where

are the Roots and

(11)

The discriminant of a Quartic Equation

(12)

(Beeler et al. 1972, Item 4).

See also Resultant

References

Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

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