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Diketahui polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus 2 x squared minus x plus p end style. Jika undefined, tentukan nilai begin mathsize 14px style 2 f left parenthesis 1 right parenthesis plus f left parenthesis 4 right parenthesis end style.

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A. Damanhuri

Master Teacher

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style 2 f left parenthesis 1 right parenthesis plus f left parenthesis 4 right parenthesis equals negative 24 plus 18 equals negative 6 end style

Pembahasan

Polinomial begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus 2 x squared minus x plus p end style dan begin mathsize 14px style f left parenthesis negative 2 right parenthesis equals 2 times f left parenthesis negative 1 right parenthesis end style,
Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x cubed minus 2 x squared minus x plus p end cell row cell f left parenthesis negative 2 right parenthesis end cell equals cell 2 times f left parenthesis negative 1 right parenthesis end cell row cell left parenthesis negative 2 right parenthesis cubed minus 2 times left parenthesis negative 2 right parenthesis squared minus left parenthesis negative 2 right parenthesis plus p end cell equals cell 2 times left parenthesis left parenthesis negative 1 right parenthesis cubed minus 2 times left parenthesis negative 1 right parenthesis squared minus left parenthesis negative 1 right parenthesis plus p right parenthesis end cell row cell negative 8 minus 8 plus 2 plus p end cell equals cell 2 times left parenthesis negative 1 minus 2 plus 1 plus p right parenthesis end cell row cell p minus 14 end cell equals cell negative 4 plus 2 p end cell row cell p minus 2 p end cell equals cell 14 minus 4 end cell row cell negative p end cell equals 10 row p equals cell negative 10 end cell end table end style 

Polinomialnya menjadi begin mathsize 14px style f left parenthesis x right parenthesis equals x cubed minus 2 x squared minus x minus 10 end style 
Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell bullet 2 f left parenthesis 1 right parenthesis end cell equals cell 2 times left parenthesis 1 cubed minus 2 times 1 squared minus 1 minus 10 right parenthesis end cell row blank equals cell 2 left parenthesis negative 12 right parenthesis end cell row blank equals cell negative 24 end cell row blank blank blank row cell bullet f left parenthesis 4 right parenthesis end cell equals cell 4 blank cubed minus 2 times 4 blank squared minus 4 minus 10 end cell row blank equals cell 64 minus 32 minus 4 minus 10 end cell row blank equals 18 end table end style 

Jadi, nilai begin mathsize 14px style 2 f left parenthesis 1 right parenthesis plus f left parenthesis 4 right parenthesis equals negative 24 plus 18 equals negative 6 end style

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