discriminant

dis·crim·i·nant

D0262800 (dĭ-skrĭm′ə-nənt)n. An expression used to distinguish or separate other expressions in a quantity or equation.

discriminant

(dɪˈskrɪmɪnənt) n (Mathematics) an algebraic expression related to the coefficients of a polynomial equation whose value gives information about the roots of the polynomial: b² – 4ac is the discriminant of ax² + bx + c = 0.

dis•crim•i•nant

(dɪˈskrɪm ə nənt)

n. a relatively simple mathematical expression that determines some of the properties, as the nature of the roots, of a given equation or function. [1830–40; < Latin discrīminant-, s. of discrīmināns, present participle of discrīmināre to divide up, separate]

Translations

дискриминант

Discriminant

discriminant

[di′skrim·ə·nənt] (mathematics) The quantity b ²- 4 ac, where a,b,c are coefficients of a given quadratic polynomial: ax ²+ bx + c. More generally, for the polynomial equation a₀ xⁿ + a₁ xⁿ ^-1+···+ a_nx₀= 0, a₀^{2 n-2}times the product of the squares of all the differences of the roots of the equation, taken in pairs.

Discriminant

The discriminant of a polynomial

P(x) = a₀xⁿ + a₁xⁿ⁻¹ + … + a_n

is the expression

in which the product is distributed over all possible differences of the roots α₁, β₂, … , α_n of the equation P (x) = 0. The discriminant vanishes if and only if there are equal roots among the roots of the polynomial. The discriminant can be expressed through the coefficients of the polynomial P(x) by representing it in the form of a determinant consisting of these coefficients. Thus, for the second-degree polynomial ax² + bx + c, the discriminant is b² − 4ac. For x³ + px + q, the discriminant is −4p³ −27q². The discriminant differs only by a factor a₀ from the resultant R(P, P′) of the polynomial P(x) and its derivative P′(x).

单词	discriminant
释义	discriminant dis·crim·i·nant D0262800 (dĭ-skrĭm′ə-nənt)n. An expression used to distinguish or separate other expressions in a quantity or equation. discriminant (dɪˈskrɪmɪnənt) n (Mathematics) an algebraic expression related to the coefficients of a polynomial equation whose value gives information about the roots of the polynomial: b² – 4ac is the discriminant of ax² + bx + c = 0. dis•crim•i•nant (dɪˈskrɪm ə nənt) n. a relatively simple mathematical expression that determines some of the properties, as the nature of the roots, of a given equation or function. [1830–40; < Latin discrīminant-, s. of discrīmināns, present participle of discrīmināre to divide up, separate] Translations дискриминант Discriminant discriminant [di′skrim·ə·nənt] (mathematics) The quantity b ²- 4 ac, where a,b,c are coefficients of a given quadratic polynomial: ax ²+ bx + c. More generally, for the polynomial equation a₀ xⁿ + a₁ xⁿ ^-1+···+ a_nx₀= 0, a₀^{2 n-2}times the product of the squares of all the differences of the roots of the equation, taken in pairs. Discriminant The discriminant of a polynomial P(x) = a₀xⁿ + a₁xⁿ⁻¹ + … + a_n is the expression in which the product is distributed over all possible differences of the roots α₁, β₂, … , α_n of the equation P (x) = 0. The discriminant vanishes if and only if there are equal roots among the roots of the polynomial. The discriminant can be expressed through the coefficients of the polynomial P(x) by representing it in the form of a determinant consisting of these coefficients. Thus, for the second-degree polynomial ax² + bx + c, the discriminant is b² − 4ac. For x³ + px + q, the discriminant is −4p³ −27q². The discriminant differs only by a factor a₀ from the resultant R(P, P′) of the polynomial P(x) and its derivative P′(x).
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