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Suku banyak p(x)=(x−a)5+(x−b)4+(x−c) habis dibagi oleh x2−(a+b)x+ab. Jika a−c=1, maka b=....

Pertanyaan

Suku banyak p open parentheses x close parentheses equals open parentheses x minus a close parentheses to the power of 5 plus open parentheses x minus b close parentheses to the power of 4 plus open parentheses x minus c close parentheses habis dibagi oleh x squared minus open parentheses a plus b close parentheses x plus a b. Jika a minus c not equal to 1, maka b equals.... 

  1. fraction numerator c minus a c plus a squared over denominator c plus 1 minus a end fraction 

  2. fraction numerator c squared plus a c minus a over denominator c plus 1 minus a end fraction 

  3. fraction numerator c plus 2 a c minus a squared over denominator c plus 1 minus a end fraction 

  4. fraction numerator 2 c squared plus a c minus a squared over denominator c plus 1 minus a end fraction 

  5. fraction numerator c plus a c minus a squared over denominator c plus 1 minus a end fraction 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Diketahui p open parentheses x close parentheses equals open parentheses x minus a close parentheses to the power of 5 plus open parentheses x minus b close parentheses to the power of 4 plus open parentheses x minus c close parentheses habis dibagi oleh x squared minus open parentheses a plus b close parentheses x plus a b dengan a minus c not equal to 1. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus open parentheses a plus b close parentheses x plus a b end cell equals 0 row cell open parentheses x minus a close parentheses open parentheses x minus b close parentheses end cell equals blank row x equals cell a space atau space x equals b end cell end table 

Sehingga:

  • Persamaan (1)

table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses a close parentheses end cell equals 0 row cell open parentheses a minus a close parentheses to the power of 5 plus open parentheses a minus b close parentheses to the power of 4 plus open parentheses a minus c close parentheses end cell equals 0 row cell 0 to the power of 5 plus open parentheses a minus b close parentheses to the power of 4 plus open parentheses a minus c close parentheses end cell equals 0 row cell open parentheses a minus b close parentheses to the power of 4 plus open parentheses a minus c close parentheses end cell equals 0 row cell open parentheses a minus b close parentheses to the power of 4 end cell equals cell negative open parentheses a minus c close parentheses end cell row cell open parentheses negative open parentheses a minus b close parentheses close parentheses to the power of 4 end cell equals cell open parentheses c minus a close parentheses end cell row cell open parentheses b minus a close parentheses to the power of 4 end cell equals cell open parentheses c minus a close parentheses end cell end table 

  • Persamaan (2)

table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses b close parentheses end cell equals 0 row cell open parentheses b minus a close parentheses to the power of 5 plus open parentheses b minus b close parentheses to the power of 4 plus open parentheses b minus c close parentheses end cell equals 0 row cell open parentheses b minus a close parentheses to the power of 5 plus 0 to the power of 4 plus open parentheses b minus c close parentheses end cell equals 0 row cell open parentheses b minus a close parentheses to the power of 5 plus open parentheses b minus c close parentheses end cell equals 0 row cell open parentheses b minus a close parentheses to the power of 4 open parentheses b minus a close parentheses plus b minus c end cell equals 0 end table 

Dengan demikian substitusikan persamaan (1) ke (2) seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses b minus a close parentheses to the power of 4 open parentheses b minus a close parentheses plus b minus c end cell equals 0 row cell open parentheses c minus a close parentheses open parentheses b minus a close parentheses plus b minus c end cell equals 0 row cell b open parentheses c minus a close parentheses minus a open parentheses c minus a close parentheses plus b minus c end cell equals 0 row cell b open parentheses c minus a close parentheses plus b end cell equals cell a open parentheses c minus a close parentheses plus c end cell row cell b open parentheses c minus a plus 1 close parentheses end cell equals cell a c minus a squared plus c end cell row b equals cell fraction numerator a c minus a squared plus c over denominator c minus a plus 1 end fraction end cell row b equals cell fraction numerator c plus a c minus a squared over denominator c minus a plus 1 end fraction end cell end table 

Jadi, jawaban yang benar adalah E.

239

4.0 (2 rating)

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