Diketahui suku banyak p(x) = 2^4+ax^3-3x^2+5x+b . Jika p(x) dibagi (x-1) sisa 11, dibagi (x+1) sisa -1 . Tentukan nilai (2a+b)
Matematika
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Pertanyaan
Diketahui suku banyak p(x) = 2^4+ax^3-3x^2+5x+b . Jika p(x) dibagi (x-1) sisa 11, dibagi (x+1) sisa -1 . Tentukan nilai (2a+b)
1 Jawaban
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1. Jawaban whongaliem
dasar : f (x) : (x - a) ⇒ sisa = f (a)
dibagi (x - 1) ⇒ sisa = f (1)
dibagi (x + 1) ⇒ sisa = f (- 1)
p (x) = 2x^4 + ax³ - 3x² + 5x + b
p (1) = 2 (1)^4 + a(1)³ - 3(1)² + 5(1) + b
11 = 2 .1 + a .1 - 3 + 5 + b
11 = 2 + a - 3 + 5 + b
11 = 4 + a + b
11 - 4 = a + b
7 = a + b ....... pers 1
p (- 1) = 2 (- 1)^4 + a(-1)³ - 3(- 1)² + 5 (- 1) + b
- 1 = 2 . 1 + a (- 1) - 3 . 1 - 5 + b
- 1 = 2 - a - 3 - 5 + b
- 1 = - 6 - a + b
6 - 1 = - a + b .... pers 2
elemenasi pers 1 dan 2
7 = a + b
5 = - a + b
---------------- +
12 = 2b
b = 12/2
b = 6
7 = a + b
7 = a + 6
a = 7 - 6
a = 1
2a + b = 2 (1) + 6
= 2 + 6
= 8