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Diketahui  adalah akar-akar persamaan polinomial . Jika  nilai  adalah....

Pertanyaan

Diketahui undefined adalah akar-akar persamaan polinomial begin mathsize 14px style x cubed minus 2 x squared minus 5 x plus p equals 0 end style. Jika begin mathsize 14px style x subscript 3 equals x subscript 2 minus x subscript 1 end style nilai begin mathsize 14px style p end style adalah....

  1. begin mathsize 14px style 6 end style 

  2. begin mathsize 14px style 5 end style 

  3. begin mathsize 14px style 4 end style 

  4. begin mathsize 14px style negative 4 end style 

  5. undefined 

Pembahasan Video:

Pembahasan Soal:

Ingat: Jika begin mathsize 14px style x subscript 1 comma space x subscript 2 comma space dan space x subscript 3 end style adalah akar-akar dari  begin mathsize 14px style straight a x cubed plus straight b x squared plus straight c x plus straight d equals 0 end style 
Maka

  •  begin mathsize 14px style x subscript 1 plus x subscript 2 plus x subscript 3 equals fraction numerator negative straight b over denominator straight a end fraction end style 
  • begin mathsize 14px style x subscript 1 times x subscript 2 plus x subscript 1 times x subscript 3 plus x subscript 2 times x subscript 3 equals straight c over straight a end style 
  • begin mathsize 14px style x subscript 1 times x subscript 2 times x subscript 3 equals fraction numerator negative straight d over denominator straight a end fraction end style

Sehingga:
Persamaan polinomial size 14px x to the power of size 14px 3 size 14px minus size 14px 2 size 14px x to the power of size 14px 2 size 14px minus size 14px 5 size 14px x size 14px plus size 14px p size 14px equals size 14px 0 dengan begin mathsize 14px style x subscript 3 equals x subscript 2 minus x subscript 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 plus x subscript 3 end cell equals cell fraction numerator negative left parenthesis negative 2 right parenthesis over denominator 1 end fraction end cell row cell x subscript 1 plus x subscript 2 plus x subscript 2 minus x subscript 1 end cell equals 2 row cell 2 x subscript 2 end cell equals 2 row cell x subscript 2 end cell equals 1 end table end style 

atau 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 3 end cell equals cell 2 minus x subscript 2 end cell row blank equals cell 2 minus 1 end cell row blank equals 1 end table end style 

Subsitusi begin mathsize 14px style x subscript 2 equals 1 end style dan begin mathsize 14px style x subscript 1 plus x subscript 3 equals 1 end style pada persamaan berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 plus x subscript 1 times x subscript 3 plus x subscript 2 times x subscript 3 end cell equals cell fraction numerator negative 5 over denominator 1 end fraction end cell row cell x subscript 1 times 1 plus x subscript 1 times x subscript 3 plus 1 times x subscript 3 end cell equals cell negative 5 end cell row cell x subscript 1 plus x subscript 3 plus x subscript 1 times x subscript 3 end cell equals cell negative 5 end cell row cell 1 plus x subscript 1 times x subscript 3 end cell equals cell negative 5 end cell row cell x subscript 1 times x subscript 3 end cell equals cell negative 5 minus 1 end cell row blank equals cell negative 6 end cell end table end style 

Substitusi nilaiundefined dan begin mathsize 14px style x subscript 1 times x subscript 3 equals negative 6 end style pada perkalian akar-akar polinom derajat tiga.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x subscript 2 times x subscript 3 end cell equals cell fraction numerator negative p over denominator 1 end fraction end cell row cell x subscript 1 times x subscript 3 times x subscript 2 end cell equals cell negative p end cell row cell negative 6 times 1 end cell equals cell negative p end cell row p equals 6 end table end style 

Jadi jawaban yang tepat adalah A

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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