Jawab:
suku banyak
Hasil bagi dan Sisa
Penjelasan dengan langkah-langkah:
misal g(x) = f(x) . (x + 1) --> g(x) habis dibagi ( x - 1)
i) g(x) = x⁴ + ax³ + (b -10)x² + 24x - 15
habis dibagi ( x - 1) , sisa = 0 --> g(1) =0
1 + a + b -10 + 24 - 15 = 0
a + b = 0 --> atau a = - b ...(i)
ii) g(x) = f(x) . (x - 1)
g'(x) = f'(x) . (x - 1) + 1. f(x)
g'(x) = 4x³+ 3a x² + 2(b -10) x + 24
f(x) habis dibagi (x - 1) --> f(1)= 0
g'(1) = f'(1) (1-1) + f (1)
g'(1) = f(1)
4(1)³ + 3a (1)² + 2(b-10)(1) + 24 = 0
4 + 3a + 2b - 20 + 24 = 0
3a + 2b = -8...(ii)
iii) pers (i ) sub ke (ii)
3 (-b) + 2b = -8
- b = - 8
b = 8
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Jawab:
suku banyak
Hasil bagi dan Sisa
Penjelasan dengan langkah-langkah:
misal g(x) = f(x) . (x + 1) --> g(x) habis dibagi ( x - 1)
i) g(x) = x⁴ + ax³ + (b -10)x² + 24x - 15
habis dibagi ( x - 1) , sisa = 0 --> g(1) =0
1 + a + b -10 + 24 - 15 = 0
a + b = 0 --> atau a = - b ...(i)
ii) g(x) = f(x) . (x - 1)
g'(x) = f'(x) . (x - 1) + 1. f(x)
g'(x) = 4x³+ 3a x² + 2(b -10) x + 24
f(x) habis dibagi (x - 1) --> f(1)= 0
g'(1) = f'(1) (1-1) + f (1)
g'(1) = f(1)
4(1)³ + 3a (1)² + 2(b-10)(1) + 24 = 0
4 + 3a + 2b - 20 + 24 = 0
3a + 2b = -8...(ii)
iii) pers (i ) sub ke (ii)
3 (-b) + 2b = -8
- b = - 8
b = 8