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Diketahui polinomial  dan . Jika  dan  bernilai sama untuk , tentukan:  b. nilai .

Pertanyaan

Diketahui polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals 2 x cubed minus 5 x squared minus x plus 3 end style dan
begin mathsize 14px style q left parenthesis x right parenthesis equals 4 x squared minus 2 x plus straight a end style. Jika begin mathsize 14px style p left parenthesis x right parenthesis end style dan begin mathsize 14px style q left parenthesis x right parenthesis end style bernilai sama untuk begin mathsize 14px style x equals negative 2 end style, tentukan: 
b. nilai size 14px 4 size 14px p size 14px left parenthesis size 14px 3 size 14px right parenthesis size 14px plus size 14px q size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis.

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Pembahasan Video:

Pembahasan Soal:

Diketahui begin mathsize 14px style p open parentheses x close parentheses equals 2 x cubed minus 5 x squared minus x plus 3 comma space q open parentheses x close parentheses equals 4 x squared minus 2 x plus a end style, dan begin mathsize 14px style p open parentheses negative 2 close parentheses equals q open parentheses negative 2 close parentheses end style, maka:

begin mathsize 14px style space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space p left parenthesis negative 2 right parenthesis equals q left parenthesis negative 2 right parenthesis 2 left parenthesis negative 2 right parenthesis cubed minus 5 left parenthesis negative 2 right parenthesis squared minus left parenthesis negative 2 right parenthesis plus 3 equals 4 left parenthesis negative 2 right parenthesis squared minus 2 left parenthesis negative 2 right parenthesis plus a space space space space space space 2 left parenthesis negative 8 right parenthesis minus 5 left parenthesis 4 right parenthesis minus left parenthesis negative 2 right parenthesis plus 3 equals 4 left parenthesis 4 right parenthesis minus 2 left parenthesis negative 2 right parenthesis plus a space space space space space space space space space space space space space space space space space minus 16 minus 20 plus 2 plus 3 equals 16 plus 4 plus a space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 31 equals 20 plus a space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 20 plus a equals negative 31 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space a equals negative 31 minus 20 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space a equals negative 51 end style 

Sehingga:

begin mathsize 14px style p open parentheses x close parentheses equals 2 x cubed minus 5 x squared minus x plus 3 p open parentheses 3 close parentheses equals 2 open parentheses 3 close parentheses cubed minus 5 open parentheses 3 close parentheses squared minus open parentheses 3 close parentheses plus 3 p open parentheses 3 close parentheses equals 2 open parentheses 27 close parentheses minus 5 open parentheses 9 close parentheses minus 3 plus 3 p open parentheses 3 close parentheses equals 54 minus 45 minus 3 plus 3 p open parentheses 3 close parentheses equals 9 end style dan,

begin mathsize 14px style q open parentheses x close parentheses equals 4 x squared minus 2 x plus a q open parentheses x close parentheses equals 4 x squared minus 2 x minus 51 q open parentheses negative 1 close parentheses equals 4 open parentheses negative 1 close parentheses squared minus 2 open parentheses negative 1 close parentheses minus 51 q open parentheses negative 1 close parentheses equals 4 open parentheses 1 close parentheses plus 2 minus 51 q open parentheses negative 1 close parentheses equals 4 plus 2 minus 51 q open parentheses negative 1 close parentheses equals negative 45 end style 

dari hasil yang di atas dapat kita hitung:

begin mathsize 14px style 4 p open parentheses 3 close parentheses plus q open parentheses negative 1 close parentheses equals 4 times 9 plus open parentheses negative 45 close parentheses equals 36 minus 45 equals negative 9 end style 

Jadi, jawaban yang benar adalah begin mathsize 14px style negative 9 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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