при каких N и M многочлен Nx^3+Mx^2+23x+15 делится на многочлен x^2+4x-5 без остатка. Created by еддпмаад. algebra-ru

Nx³ + Mx² + 23x + 15 |x²+4x-5Nx² + 4Nx² - 5Nx Nx+(M-4N)------------------------------------ (M-4N)x²+(23+5N)x+15 (M-4N)x²+(4M-16N)x-(5M-20N) --------------------------------------------- 0{23+5N=4M-16N⇒21N-4M+23=0{15=-5M+20N⇒5M=20N-15⇒M=4N-321N-4*(4N-3)+23=021N-16N+12+23=05N=-35N=-7M=4*(-7)-3=-28-3=-31------------------------------------------------7x³-31x²+23x+15 |x²+4x-5-7x³-28x²+35x -7x-3------------------------ -3x²-12x+15 -3x²-12x+15 ------------------- 0 Новые вопросы в Алгебра При каких значениях а система уравнений не имеет решений a ≠ 9 a ≠ -5 a ≠ -9 a ≠ 5 Побудуй графік функції у = 1,5х + 2. Визнач за графіком: а) значення у, якщо x = -4: б) значення х, якщо у = -1. помогите срочно пжпжп Решите уравнения а) (x^2-1)(x^2+3)=(x^2+1^2)+x б) y^3+3y^2-y-3=0 натуральні числа a, b є такими що НСК (a;b)=169 знайдіть a, b. помогите!! Срочно!! Пожалуйста!!!Знайдіть суму перших п'яти членів арифметичної прогрес (а), якщо a = -10, d=25. СРОЧНО ПОМОЖІТЬ При якому k графік лінійної функції y=kx+18 паралельний до графіка функції y=5x-9 * -9 5 18 -5 4. Кут між висотою ск та катетом СА прямокутного трикутника ABC (4C = 90°) дорівнює 33°. Знайди гострі кути трикутника ABC. Срочно!!!!!!!!!!!!! Знайти добуток коренів (x-5)(2x+1)=0 ПОМОГИТЕ Помогити пж.................... Предыдущий Следующий Вместе мы знаем больше Этот сайт использует cookies Политика Cookies . Вы можете указать условия хранения и доступ к cookies в своем браузере. 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при каких N и M многочлен Nx^3+Mx^2+23x+15 делится на многочлен x^2+4x-5 без ост...

еддпмаад @еддпмаад

March 2022 1 44 Report

при каких N и M многочлен Nx^3+Mx^2+23x+15 делится на многочлен x^2+4x-5 без остатка

Answers & Comments

sedinalana

Verified answer

Nx³ + Mx² + 23x + 15 |x²+4x-5
Nx² + 4Nx² - 5Nx Nx+(M-4N)
------------------------------------
(M-4N)x²+(23+5N)x+15
   (M-4N)x²+(4M-16N)x-(5M-20N)
   ---------------------------------------------
   0
{23+5N=4M-16N⇒21N-4M+23=0
{15=-5M+20N⇒5M=20N-15⇒M=4N-3
21N-4*(4N-3)+23=0
21N-16N+12+23=0
5N=-35
N=-7
M=4*(-7)-3=-28-3=-31
-----------------------------------------------
-7x³-31x²+23x+15 |x²+4x-5
-7x³-28x²+35x -7x-3
------------------------
   -3x²-12x+15
   -3x²-12x+15
   -------------------
   0