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Tentukan akar-akar dari persamaan polinomial .

Pertanyaan

Tentukan akar-akar dari persamaan polinomial begin mathsize 14px style 36 x to the power of 5 minus 36 x to the power of 4 minus 13 x cubed plus 13 x squared plus x minus 1 equals 0 end style

  1. undefined 

  2. undefined 

Pembahasan Video:

Pembahasan Soal:

Persamaan: begin mathsize 14px style 36 x to the power of 5 minus 36 x to the power of 4 minus 13 x cubed plus 13 x squared plus x minus 1 equals 0 end style.

Error converting from MathML to accessible text.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank Suku end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank konstan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank adalah end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank p end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell space minus 1 space left parenthesis faktor space dari space minus 1 space adalah space plus-or-minus 1 right parenthesis. end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank Akar end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank yang end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank mungkin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank adalah end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell p over q end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 1 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 6 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 9 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 12 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 18 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank dan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 36 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table end style  

 

Uji untuk undefined

 

Karena sisa = 0, maka diperoleh begin mathsize 14px style x equals 1 end style merupakan salah satu akarnya.

Hasil bagi begin mathsize 14px style 36 x to the power of 4 minus 13 x squared plus 1 end style  

Uji untuk undefined

  

Karena sisa = 0, maka diperoleh begin mathsize 14px style x equals 1 half end style merupakan salah satu akarnya.

Hasil bagi begin mathsize 14px style 36 x cubed plus 18 x squared minus 4 x minus 2 end style

Uji untuk begin mathsize 14px style x equals negative 1 half end style 

 

Karena sisa = 0, maka diperoleh begin mathsize 14px style x equals negative 1 half end style merupakan salah satu akarnya.

Hasil bagi begin mathsize 14px style 36 x squared minus 4 end style.

Mencari akar lainnya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 36 x squared minus 4 end cell equals 0 row cell 36 x squared end cell equals 4 row cell x squared end cell equals cell 1 over 9 end cell row x equals cell plus-or-minus square root of 1 over 9 end root end cell row x equals cell plus-or-minus 1 third end cell end table end style 

Jadi, akar-akar persamaan polinomial adalah begin mathsize 14px style 1 comma space 1 half comma space minus 1 half comma space 1 third comma space dan space minus 1 third end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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