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Tentukan akar-akar dari persamaan polinomial .

Pertanyaan

Tentukan akar-akar dari persamaan polinomial begin mathsize 14px style 2 x to the power of 4 plus 3 x cubed minus 14 x squared minus 3 x plus 2 equals 0 end style

  1. begin mathsize 14px style.... end style 

  2. undefined 

Pembahasan Video:

Pembahasan Soal:

Terdapat kesalahan pada soal. Persamaan yang dimaksud bukan begin mathsize 14px style 2 x to the power of 4 plus 3 x cubed minus 14 x squared minus 3 x plus 2 equals 0 end style, melainkan begin mathsize 14px style 2 x to the power of 4 plus 3 x cubed minus 4 x squared minus 3 x plus 2 equals 0 end style.

Persamaan: begin mathsize 14px style 2 x to the power of 4 plus 3 x cubed minus 4 x squared minus 3 x plus 2 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 2 space left parenthesis faktor space dari space 2 space adalah space plus-or-minus 1 comma space dan space plus-or-minus 2 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 straight p over straight 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 2 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 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 2 over 2 end cell end table end style  

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

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x to the power of 4 plus 3 x cubed minus 4 x squared minus 3 x plus 2 end cell equals cell 2 times 1 to the power of 4 plus 3 times 1 cubed minus 4 times 1 squared minus 3 times 1 plus 2 end cell row blank equals cell 2 plus 3 minus 4 minus 3 plus 2 end cell row blank equals 0 end table end style 

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

Uji untuk undefined

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x to the power of 4 plus 3 x cubed minus 4 x squared minus 3 x plus 2 end cell equals cell 2 times left parenthesis negative 2 right parenthesis to the power of 4 plus 3 times left parenthesis negative 2 right parenthesis cubed minus 4 times left parenthesis negative 2 right parenthesis squared minus 3 times left parenthesis negative 2 right parenthesis plus 2 end cell row blank equals cell 32 minus 24 minus 16 plus 6 plus 2 end cell row blank equals 0 end table end style

Karena sisa = 0, maka diperoleh begin mathsize 14px style x equals negative 2 end style merupakan salah satu akarnya.

Persamaan menjadi

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x to the power of 4 plus 3 x cubed minus 4 x squared minus 3 x plus 2 end cell equals 0 row cell left parenthesis x minus 1 right parenthesis left parenthesis x plus 2 right parenthesis times h left parenthesis x right parenthesis end cell equals 0 row cell left parenthesis x squared plus x minus 2 right parenthesis left parenthesis 2 x squared plus x minus 1 right parenthesis end cell equals 0 row cell left parenthesis x squared plus x minus 2 right parenthesis left parenthesis 2 x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis end cell equals 0 end table end style 

Diperoleh akar lainnya yaitu begin mathsize 14px style x equals 1 half space dan space x equals negative 1 end style

Jadi, akar-akar persamaan tersebut adalahbegin mathsize 14px style 1 comma space minus 1 comma space minus 2 comma space dan space 1 half end style.

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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