1. Diketahui f ( x ) = ( x 4 − 4 x 3 + a x 2 + b x + 6 ) d an g ( x ) = ( x 3 + 2 x 2 + c x + 12 ) 2. Misalkan a = − 1 , b = 10 , c = 6 sehingga f ( x ) = ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) d an g ( x ) = ( x 3 + 2 x 2 + 6 x + 12 ) 3. Operasi: f ( x ) + g ( x ) = ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) + ( x 3 + 2 x 2 + 6 x + 12 ) = x 4 − 4 x 3 − x 2 + 10 x + 6 + x 3 + 2 x 2 + 6 x + 12 = x 4 − 4 x 3 + x 3 − x 2 + 2 x 2 + 10 x + 6 x + 6 + 12 = x 4 − 4 x 3 + x 3 + x 2 + 10 x + 6 x + 6 + 12 = x 4 − 3 x 3 + x 2 + 10 x + 6 x + 6 + 12 = x 4 − 3 x 3 + x 2 + 16 x + 6 + 12 = x 4 − 3 x 3 + x 2 + 16 x + 18 Der aja t 4 f ( x ) − g ( x ) = ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) − ( x 3 + 2 x 2 + 6 x + 12 ) = x 4 − 4 x 3 − x 2 + 10 x + 6 − ( x 3 + 2 x 2 + 6 x + 12 ) = x 4 − 4 x 3 − x 2 + 10 x + 6 − x 3 − 2 x 2 − 6 x − 12 = x 4 − 4 x 3 − x 3 − x 2 − 2 x 2 + 10 x − 6 x + 6 − 12 = x 4 − 4 x 3 − x 3 − x 2 − 2 x 2 + 10 x − 6 x + 6 − 12 = x 4 − 5 x 3 − 3 x 2 + 10 x − 6 x + 6 − 12 = x 4 − 5 x 3 − 3 x 2 + 4 x + 6 − 12 = x 4 − 5 x 3 − 3 x 2 + 4 x − 6 Derajat 4 g ( x ) − f ( x ) = ( x 3 + 2 x 2 + 6 x + 12 ) − ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) = x 3 + 2 x 2 + 6 x + 12 − ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) = x 3 + 2 x 2 + 6 x + 12 − x 4 + 4 x 3 + x 2 − 10 x − 6 = − x 4 + x 3 + 4 x 3 + 2 x 2 + x 2 + 6 x − 10 x + 12 − 6 = − x 4 + x 3 + 4 x 3 + 3 x 2 + 6 x − 10 x + 12 − 6 = − x 4 + 5 x 3 + 3 x 2 + 6 x − 10 x + 12 − 6 = − x 4 + 5 x 3 + 3 x 2 − 4 x + 12 − 6 = − x 4 + 5 x 3 + 3 x 2 − 4 x + 6 Der aja t 4 Derajat 7 g ( x ) f ( x ) = = ( x 3 + 2 x 2 + 6 x + 12 ) ( x 4 − 4 x 3 − x 2 + 10 x + 6 ) = x + x 3 + 2 x 2 + 6 x + 12 − 6 x 3 − 7 x 2 − 2 x + 6 = x − 6 + x 3 + 2 x 2 + 6 x + 12 5 x 2 + 34 x + 78 Derajat 3 Derajat 8 f ( x 2 ) = ( x 2 ) 4 − 4 ( x 2 ) 3 − ( x 2 ) 2 + 10 x 2 + 6 = x 8 − 4 x 6 − x 4 + 10 x 2 + 6 Derajat 8 Derajat 6 g ( x 2 ) = ( x 2 ) 3 + 2 ( x 2 ) 2 + 6 x 2 + 12 = x 6 + 2 x 4 + 6 x 2 + 12 Derajat 6 AKAR AKAR f(x)+g(x)=0 x 4 − 3 x 3 + x 2 + 16 x + 18 = 0 T i d ak a d a so l u s i aka r − aka r f ( x ) − g ( x ) = 0 x 4 − 5 x 3 − 3 x 2 + 4 x − 6 = 0 M e n u r u t x n + 1 = x n + 4 m u − + 4 m u f + 4 m u ( x n ) f ( x n ) x 3 − 6.39707 … x 2 + 5.93718 … x − 4.29468 ⋯ ≈ + 4 m u 0 x 2 − 0.94441 … x + 0.78763 ⋯ ≈ + 4 m u 0 A ka r − aka r m y a x ≈ + 4 m u − 1.39707 … , + 4 m ux ≈ + 4 m u 5.45266 … g ( x ) − f ( x ) = 0 0 = − x 4 + 5 x 3 + 3 x 2 − 4 x + 6 M e n u r u t x n + 1 = x n + 4 m u − + 4 m u f + 4 m u ( x n ) f ( x n ) − x 3 + 6.39707 … x 2 − 5.93718 … x + 4.29468 ⋯ ≈ + 4 m u 0 − x 2 + 0.94441 … x − 0.78763 ⋯ ≈ + 4 m u 0 x ≈ + 4 m u − 1.39707 … , + 4 m ux ≈ + 4 m u 5.45266 … f ( x ) . g ( x ) = 0 0 = ( x + 1 ) x + 1 x 7 − 2 x 6 − 3 x 5 − 4 x 4 − 28 x 3 + 60 x 2 + 156 x + 72 0 = ( x + 1 ) x 6 + x + 1 − 3 x 6 − 3 x 5 − 4 x 4 − 28 x 3 + 60 x 2 + 156 x + 72 0 = ( x + 1 ) x 6 − 3 x 5 + x + 1 − 4 x 4 − 28 x 3 + 60 x 2 + 156 x + 72 0 = ( x + 1 ) x 6 − 3 x 5 − 4 x 3 + x + 1 − 24 x 3 + 60 x 2 + 156 x + 72 0 = ( x + 1 ) x 6 − 3 x 5 − 4 x 3 − 24 x 2 + x + 1 84 x 2 + 156 x + 72 0 = ( x + 1 ) x 6 − 3 x 5 − 4 x 3 − 24 x 2 + 84 x + x + 1 72 x + 72 0 = ( x + 1 ) x 6 − 3 x 5 − 4 x 3 − 24 x 2 + 84 x + 72 0 = ( x + 1 ) ( x + 2 ) ( x − 3 ) ( x 4 − 2 x 3 + 4 x 2 − 12 x − 12 ) x + 1 = 0 a t a u + 4 m ux + 2 = 0 a t a u + 4 m ux − 3 = 0 a t a u + 4 m u x 4 − 2 x 3 + 4 x 2 − 12 x − 12 = 0 Akar-akarnya adalah x = − 1 , + 4 m ux = − 2 , + 4 m ux = 3 , + 4 m u x = − 3 + 1 , + 4 m ux = 3 + 1 g ( x ) f ( x ) 0 0 ⋅ 0 0 0 x = = = = = = = 0 x − 6 + x 3 + 2 x 2 + 6 x + 12 5 x 2 + 34 x + 78 x ( x 3 + 2 x 2 + 6 x + 12 ) − 6 ( x 3 + 2 x 2 + 6 x + 12 ) + x 3 + 2 x 2 + 6 x + 12 5 x 2 + 34 x + 78 ( x 3 + 2 x 2 + 6 x + 12 ) x ( x 3 + 2 x 2 + 6 x + 12 ) − 6 ( x 3 + 2 x 2 + 6 x + 12 ) + 5 x 2 + 34 x + 78 x 4 − 4 x 3 − x 2 + 10 x + 6 ( x + 1 ) ( x − 3 ) ( x 2 − 2 x − 2 ) A ka r aka r n y a − 1 , + 4 m ux = 3 , + 4 m ux = 1 + 3 , + 4 m ux = 1 − 3 Akarnya adalah -2. g ( x 2 ) = 0 x 6 + 2 x 4 + 6 x 2 + 12 = 0 u = x 2 u 3 + 2 u 2 + 6 u + 12 = 0 ( u + 2 ) ( u 2 + 6 ) = 0 u + 2 = 0 or + 4 m u u 2 + 6 = 0 u = − 2 , u = x 2 x 2 = − 2 t i d ak m e m e n u hi Tidak ada akar-akar.

Question

1. Diketahui $f (x) = (x^{4} - 4 x^{3} + a x^{2} + b x + 6) d an g (x) = (x^{3} + 2 x^{2} + c x + 12)$

2. Misalkan $a = - 1, b = 10, c = 6$ sehingga

$f (x) = (x^{4} - 4 x^{3} - x^{2} + 10 x + 6) d an g (x) = (x^{3} + 2 x^{2} + 6 x + 12)$

3. Operasi:

$f (x) + g (x) = (x^{4} - 4 x^{3} - x^{2} + 10 x + 6) + (x^{3} + 2 x^{2} + 6 x + 12) = x^{4} - 4 x^{3} - x^{2} + 10 x + 6 + x^{3} + 2 x^{2} + 6 x + 12 = x^{4} - 4 x^{3} + x^{3} - x^{2} + 2 x^{2} + 10 x + 6 x + 6 + 12 = x^{4} - 4 x^{3} + x^{3} + x^{2} + 10 x + 6 x + 6 + 12 = x^{4} - 3 x^{3} + x^{2} + 10 x + 6 x + 6 + 12 = x^{4} - 3 x^{3} + x^{2} + 16 x + 6 + 12 = x^{4} - 3 x^{3} + x^{2} + 16 x + 18 Der aja t 4$

$f (x) - g (x) = (x^{4} - 4 x^{3} - x^{2} + 10 x + 6) - (x^{3} + 2 x^{2} + 6 x + 12) = x^{4} - 4 x^{3} - x^{2} + 10 x + 6 - (x^{3} + 2 x^{2} + 6 x + 12) = x^{4} - 4 x^{3} - x^{2} + 10 x + 6 - x^{3} - 2 x^{2} - 6 x - 12 = x^{4} - 4 x^{3} - x^{3} - x^{2} - 2 x^{2} + 10 x - 6 x + 6 - 12 = x^{4} - 4 x^{3} - x^{3} - x^{2} - 2 x^{2} + 10 x - 6 x + 6 - 12 = x^{4} - 5 x^{3} - 3 x^{2} + 10 x - 6 x + 6 - 12 = x^{4} - 5 x^{3} - 3 x^{2} + 4 x + 6 - 12 = x^{4} - 5 x^{3} - 3 x^{2} + 4 x - 6$

Derajat 4

$g (x) - f (x) = (x^{3} + 2 x^{2} + 6 x + 12) - (x^{4} - 4 x^{3} - x^{2} + 10 x + 6) = x^{3} + 2 x^{2} + 6 x + 12 - (x^{4} - 4 x^{3} - x^{2} + 10 x + 6) = x^{3} + 2 x^{2} + 6 x + 12 - x^{4} + 4 x^{3} + x^{2} - 10 x - 6 = - x^{4} + x^{3} + 4 x^{3} + 2 x^{2} + x^{2} + 6 x - 10 x + 12 - 6 = - x^{4} + x^{3} + 4 x^{3} + 3 x^{2} + 6 x - 10 x + 12 - 6 = - x^{4} + 5 x^{3} + 3 x^{2} + 6 x - 10 x + 12 - 6 = - x^{4} + 5 x^{3} + 3 x^{2} - 4 x + 12 - 6 = - x^{4} + 5 x^{3} + 3 x^{2} - 4 x + 6 Der aja t 4$

Derajat 7

$\frac{f ( x )}{g ( x )} = = \frac{( x ^{4} - 4 x ^{3} - x ^{2} + 10 x + 6 )}{( x ^{3} + 2 x ^{2} + 6 x + 12 )} = x + \frac{- 6 x ^{3} - 7 x ^{2} - 2 x + 6}{x ^{3} + 2 x ^{2} + 6 x + 12} = x - 6 + \frac{5 x ^{2} + 34 x + 78}{x ^{3} + 2 x ^{2} + 6 x + 12}$

Derajat 3

Derajat 8

$f (x^{2}) = (x^{2})^{4} - 4 (x^{2})^{3} - (x^{2})^{2} + 10 x^{2} + 6 = x^{8} - 4 x^{6} - x^{4} + 10 x^{2} + 6$

Derajat 8

Derajat 6

$g (x^{2}) = (x^{2})^{3} + 2 (x^{2})^{2} + 6 x^{2} + 12 = x^{6} + 2 x^{4} + 6 x^{2} + 12$

Derajat 6

AKAR AKAR

f(x)+g(x)=0

$x^{4} - 3 x^{3} + x^{2} + 16 x + 18 = 0 T i d ak a d a so l u s i aka r - aka r$

$f (x) - g (x) = 0 x^{4} - 5 x^{3} - 3 x^{2} + 4 x - 6 = 0 M e n u r u t x_{n + 1} = x_{n} + 4 m u - + 4 m u \frac{f ( x _{n} )}{f + 4 m u ( x _{n} )} x^{3} - 6.39707 \dots x^{2} + 5.93718 \dots x - 4.29468 \dots \approx + 4 m u 0 x^{2} - 0.94441 \dots x + 0.78763 \dots \approx + 4 m u 0 A ka r - aka r m y a x \approx + 4 m u - 1.39707 \dots, + 4 m ux \approx + 4 m u 5.45266 \dots$

$g (x) - f (x) = 0 0 = - x^{4} + 5 x^{3} + 3 x^{2} - 4 x + 6 M e n u r u t x_{n + 1} = x_{n} + 4 m u - + 4 m u \frac{f ( x _{n} )}{f + 4 m u ( x _{n} )} - x^{3} + 6.39707 \dots x^{2} - 5.93718 \dots x + 4.29468 \dots \approx + 4 m u 0 - x^{2} + 0.94441 \dots x - 0.78763 \dots \approx + 4 m u 0 x \approx + 4 m u - 1.39707 \dots, + 4 m ux \approx + 4 m u 5.45266 \dots$

$f (x) . g (x) = 0 0 = (x + 1) \frac{x ^{7} - 2 x ^{6} - 3 x ^{5} - 4 x ^{4} - 28 x ^{3} + 60 x ^{2} + 156 x + 72}{x + 1} 0 = (x + 1) x^{6} + \frac{- 3 x ^{6} - 3 x ^{5} - 4 x ^{4} - 28 x ^{3} + 60 x ^{2} + 156 x + 72}{x + 1} 0 = (x + 1) x^{6} - 3 x^{5} + \frac{- 4 x ^{4} - 28 x ^{3} + 60 x ^{2} + 156 x + 72}{x + 1} 0 = (x + 1) x^{6} - 3 x^{5} - 4 x^{3} + \frac{- 24 x ^{3} + 60 x ^{2} + 156 x + 72}{x + 1} 0 = (x + 1) x^{6} - 3 x^{5} - 4 x^{3} - 24 x^{2} + \frac{84 x ^{2} + 156 x + 72}{x + 1} 0 = (x + 1) x^{6} - 3 x^{5} - 4 x^{3} - 24 x^{2} + 84 x + \frac{72 x + 72}{x + 1} 0 = (x + 1) x^{6} - 3 x^{5} - 4 x^{3} - 24 x^{2} + 84 x + 72 0 = (x + 1) (x + 2) (x - 3) (x^{4} - 2 x^{3} + 4 x^{2} - 12 x - 12)$
$x + 1 = 0 a t a u + 4 m ux + 2 = 0 a t a u + 4 m ux - 3 = 0 a t a u + 4 m u x^{4} - 2 x^{3} + 4 x^{2} - 12 x - 12 = 0$

Akar-akarnya adalah
$x = - 1, + 4 m ux = - 2, + 4 m ux = 3, + 4 m u x = - 3 + 1, + 4 m ux = 3 + 1$

$\frac{f ( x )}{g ( x )} 0 0 \cdot 000 x = = = = = = = 0 x - 6 + \frac{5 x ^{2} + 34 x + 78}{x ^{3} + 2 x ^{2} + 6 x + 12} x (x^{3} + 2 x^{2} + 6 x + 12) - 6 (x^{3} + 2 x^{2} + 6 x + 12) + \frac{5 x ^{2} + 34 x + 78}{x ^{3} + 2 x ^{2} + 6 x + 12} (x^{3} + 2 x^{2} + 6 x + 12) x (x^{3} + 2 x^{2} + 6 x + 12) - 6 (x^{3} + 2 x^{2} + 6 x + 12) + 5 x^{2} + 34 x + 78 x^{4} - 4 x^{3} - x^{2} + 10 x + 6 (x + 1) (x - 3) (x^{2} - 2 x - 2) A ka r aka r n y a - 1, + 4 m ux = 3, + 4 m ux = 1 + 3, + 4 m ux = 1 - 3$

$g squared left parenthesis x right parenthesis equals 0 x to the power of 6 plus 4 x to the power of 5 plus 16 x to the power of 4 plus 48 x cubed plus 84 x squared plus 144 x plus 144 equals 0 open parentheses x plus 2 close parentheses fraction numerator x to the power of 6 plus 4 x to the power of 5 plus 16 x to the power of 4 plus 48 x cubed plus 84 x squared plus 144 x plus 144 over denominator x plus 2 end fraction equals 0 open parentheses x plus 2 close parentheses x to the power of 5 plus fraction numerator 2 x to the power of 5 plus 16 x to the power of 4 plus 48 x cubed plus 84 x squared plus 144 x plus 144 equals 0 over denominator x plus 2 end fraction open parentheses x plus 2 close parentheses x to the power of 5 plus 2 x to the power of 4 plus fraction numerator 12 x to the power of 4 plus 48 x cubed plus 84 x squared plus 144 x plus 144 over denominator x plus 2 end fraction equals 0 open parentheses x plus 2 close parentheses x to the power of 5 plus 2 x to the power of 4 plus 12 x cubed plus fraction numerator 24 x cubed plus 84 x squared plus 144 x plus 144 over denominator x plus 2 end fraction equals 0 open parentheses x plus 2 close parentheses x to the power of 5 plus 2 x to the power of 4 plus 12 x cubed plus 24 x squared plus fraction numerator 36 x squared plus 144 x plus 144 over denominator x plus 2 end fraction equals 0 open parentheses x plus 2 close parentheses x to the power of 5 plus 2 x to the power of 4 plus 12 x cubed plus 24 x squared plus 36 x plus fraction numerator 72 x plus 144 over denominator x plus 2 end fraction equals 0 open parentheses x plus 2 close parentheses x to the power of 5 plus 2 x to the power of 4 plus 12 x cubed plus 24 x squared plus 36 x plus 72 equals 0 open parentheses x plus 2 close parentheses x to the power of 4 plus 12 x squared plus 36 equals 0 left parenthesis x plus 2 right parenthesis open parentheses x plus 2 close parentheses open parentheses x plus 2 close parentheses open parentheses x squared plus 6 close parentheses open parentheses x squared plus 6 close parentheses equals 0 open parentheses x plus 2 close parentheses squared open parentheses x squared plus 6 close parentheses squared equals 0 open parentheses x plus 2 close parentheses squared equals 0 space a t a u space open parentheses x squared plus 6 close parentheses squared equals 0 x equals negative 2$

Akarnya adalah -2.

$g (x^{2}) = 0 x^{6} + 2 x^{4} + 6 x^{2} + 12 = 0 u = x^{2} u^{3} + 2 u^{2} + 6 u + 12 = 0 (u + 2) (u^{2} + 6) = 0 u + 2 = 0 or + 4 m u u^{2} + 6 = 0 u = - 2, u = x^{2} x^{2} = - 2 t i d ak m e m e n u hi$

Tidak ada akar-akar.

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