Определите A и B так, чтобы Ax^4-Bx^2-6x-3 делился на (x+1)^2. Created by SAHARIA. algebra-ru

Если многочлен четвертой степени разделить на многочлен второй степени, то получим многочлен второй степени.(Ах⁴-Вх²-6х-3):(х+1)²=(Mx²+Nx+C)илиАх⁴-Вх²-6х-3=(x+1)²·(Mx²+Nx+C)Ах⁴-Вх²-6х-3=(x²+2x+1)·(Mx²+Nx+C)Ах⁴-Вх²-6х-3=Mx⁴+Nx³+Cx²+2Mx³+2Nx²+2Cx+Mx²+Nx+CАх⁴-Вх²-6х-3=Mx⁴+(N+2M)x³+(C+2N+M)x²+(2C+N)x+CДва многочлена равны, если степени эти многочлены одной степени и коэффициенты при одинаковых степенях переменной равны.{ M=A{N+2M=0{C+2N+M=-B{2C+N=-6{C=-3N=-6-2C=-6-2·(-3)=0Тогда N+2M=0Если N=0, то M=0C=-BB=3A=M=0О т в е т. А=0; В=3Тогда-3х²-6х-3=-3·(х²+2х+1) делится на (х+1)²в ответе получим -3Новые вопросы в Алгебрапомогите пожалуйста решить методом сложения Помогите решить. х=-1 у=5 то 2х+9у-7Помогите решить. х=-1 у=5 то 2х+9у-7Помогите решить. х÷х+9=14ПЛС М+ПОМОГИТЕ, ДАМС КОРОНУ И МНОГО 30 БАЛЛОВ(Нужно объяснение)557,559 номера. Если возможно,с решением Разложить на множетелиy^8-y^4+4y^2-4Дайте відповідь з рішенням будь ласка(557,559)1) 3 1/9 : 2 1/3 - 2 5/6 =28/9 * 3/7 - 17/6=4/3-17/6= 8/6-17/6=-3/2=-1.5как он получил -3/2Іван зірвав на клумбі 8 нарцисів та 4 тюльпани. Скільки всього існуєспособів вибору із цих квітів 3 нарцисів та 2 тюльпанів для букета?ПредыдущийСледующийВместе мы знаем большеЭтот сайт использует cookies Политика Cookies . 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Определите A и B так, чтобы Ax^4-Bx^2-6x-3 делился на (x+1)^2...

SAHARIA @SAHARIA

August 2022 1 17 Report

Определите A и B так, чтобы Ax^4-Bx^2-6x-3 делился на (x+1)^2

Answers & Comments

nafanya2014

Verified answer

Если многочлен четвертой степени разделить на многочлен второй степени, то получим многочлен второй степени.

(Ах⁴-Вх²-6х-3):(х+1)²=(Mx²+Nx+C)

или
Ах⁴-Вх²-6х-3=(x+1)²·(Mx²+Nx+C)

Ах⁴-Вх²-6х-3=(x²+2x+1)·(Mx²+Nx+C)

Ах⁴-Вх²-6х-3=Mx⁴+Nx³+Cx²+2Mx³+2Nx²+2Cx+Mx²+Nx+C

Ах⁴-Вх²-6х-3=Mx⁴+(N+2M)x³+(C+2N+M)x²+(2C+N)x+C

Два многочлена равны, если степени эти многочлены одной степени и коэффициенты при одинаковых степенях переменной равны.

{ M=A
{N+2M=0
{C+2N+M=-B
{2C+N=-6
{C=-3

N=-6-2C=-6-2·(-3)=0

Тогда N+2M=0
Если N=0, то M=0
C=-B
B=3

A=M=0

О т в е т. А=0; В=3
Тогда
-3х²-6х-3=-3·(х²+2х+1) делится на (х+1)²
в ответе получим -3