Roboguru

Diketahui polinomial  dan . Jika dan, nilai  adalah ...

Pertanyaan

Diketahui polinomial begin mathsize 14px style p left parenthesis x right parenthesis equals 4 x cubed minus 2 x squared plus 1 end style dan begin mathsize 14px style q left parenthesis x right parenthesis equals x to the power of 4 minus n x squared plus 2 end style. Jika begin mathsize 14px style r left parenthesis x right parenthesis equals p left parenthesis x right parenthesis minus q left parenthesis x right parenthesis space end styledanbegin mathsize 14px style space r left parenthesis 2 right parenthesis equals 39 end style, nilai begin mathsize 14px style n end style adalah ...

  1. 8begin mathsize 14px style space end style

  2. 12begin mathsize 14px style space end style 

  3. 15begin mathsize 14px style space end style 

  4. 18 begin mathsize 14px style space end style 

  5. 20 begin mathsize 14px style space end style

Pembahasan Video:

Pembahasan Soal:

Diketahui begin mathsize 14px style p open parentheses x close parentheses equals 4 x cubed minus 2 x squared plus 1 comma space q open parentheses x close parentheses equals x to the power of 4 minus n x squared plus 2 comma space r open parentheses x close parentheses equals p open parentheses x close parentheses minus q open parentheses x close parentheses end style, dan begin mathsize 14px style r open parentheses 2 close parentheses equals 39 end style, maka:

 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px p begin mathsize 14px style left parenthesis x right parenthesis end style size 14px minus size 14px q begin mathsize 14px style left parenthesis x right parenthesis end style size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals begin mathsize 14px style left parenthesis 4 x cubed minus 2 x squared plus 1 right parenthesis end style size 14px minus begin mathsize 14px style left parenthesis x to the power of 4 minus n x squared plus 2 right parenthesis end style size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px 4 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 plus size 14px 1 size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px n size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px 4 size 14px x to the power of size 14px 3 size 14px plus size 14px n size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 1 size 14px minus size 14px 2 size 14px r begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px minus size 14px x to the power of size 14px 4 size 14px plus size 14px 4 size 14px x to the power of size 14px 3 size 14px plus begin mathsize 14px style left parenthesis n minus 2 right parenthesis end style size 14px x to the power of size 14px 2 size 14px minus size 14px 1    

Sehingga:

begin mathsize 14px style space space space space r open parentheses x close parentheses equals negative x to the power of 4 plus 4 x cubed plus open parentheses n minus 2 close parentheses x squared minus 1 space space space space r open parentheses 2 close parentheses equals negative open parentheses 2 close parentheses to the power of 4 plus 4 open parentheses 2 close parentheses cubed plus open parentheses n minus 2 close parentheses open parentheses 2 close parentheses squared minus 1 space space space space space space 39 equals negative 16 plus 4 left parenthesis 8 right parenthesis plus left parenthesis n minus 2 right parenthesis open parentheses 4 close parentheses minus 1 space space space space space space 39 equals negative 16 plus 32 plus 4 n minus 8 minus 1 space space space space space space 39 equals 4 n plus 7 4 n plus 7 equals 39 space space space space space 4 n equals 39 minus 7 space space space space space 4 n equals 32 space space space space space space space n equals 32 over 4 space space space space space space space n equals 8 end style 

Jadi, jawaban yang benar adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved