Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Pertanyaan

Nilai c yang memenuhi ( 0 , 04 ) x 2 + 3 x − c > ( 0 , 008 ) x 2 − 2 x + 5 untuk semua x adalah ....

Nilai c yang memenuhi  untuk semua x adalah ....

  1. c greater than 19 over 2

  2. c greater than 21 over 2

  3. c greater than 23 over 2

  4. c space less than 19 over 2  

  5. c space less than space 21 over 2  

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

01

:

17

:

56

:

50

Klaim

Iklan

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Karena 0 < 0,2 < 1 , maka Misalkan . Supaya untuk setiap x , maka haruslah definit positif. Suatu fungsi kuadrat merupakan definit positif apabila Pada jelas bahwa koefisien sudah positif, sehingga harus memenuhi

open parentheses 0 comma 04 close parentheses to the power of x squared plus 3 x minus c end exponent space greater than space open parentheses 0 comma 008 close parentheses to the power of x squared minus 2 x plus 5 end exponent open parentheses open parentheses 0 comma 2 close parentheses squared close parentheses to the power of x squared plus 3 x minus c end exponent space greater than open parentheses open parentheses 0 comma 2 close parentheses cubed close parentheses to the power of x squared minus 2 x plus 5 end exponent open parentheses 0 comma 2 close parentheses to the power of 2 open parentheses x squared plus 3 x minus c close parentheses end exponent space greater than open parentheses 0 comma 2 close parentheses to the power of 3 open parentheses x squared minus 2 x plus 5 close parentheses end exponent open parentheses 0 comma 2 close parentheses to the power of 2 x squared plus 6 x minus 2 c end exponent space greater than open parentheses 0 comma 2 close parentheses to the power of 3 x squared minus 6 x plus 15 end exponent  

 

Karena 0 < 0,2 < 1, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 0 comma 2 close parentheses to the power of 2 x squared plus 6 x minus 2 c end exponent space end cell greater than cell space open parentheses 0 comma 2 close parentheses to the power of 3 x squared minus 6 x plus 15 end exponent end cell row cell 2 x squared plus 6 x minus 2 c end cell less than cell 3 x squared minus 6 x plus 15 end cell row cell negative x squared plus 12 x minus 2 c minus 15 end cell less than 0 row cell x squared minus 12 x plus 2 c plus 15 end cell greater than 0 end table  

 

Misalkan f open parentheses x close parentheses equals x squared minus 12 x plus 2 c plus 15. Supaya f open parentheses x close parentheses greater than 0 untuk setiap x, maka f open parentheses x close parentheses haruslah definit positif.

Suatu fungsi kuadrat undefined merupakan definit positif apabila a greater than 0 space d a n space D less than 0.

Pada undefined jelas bahwa koefisien x squared sudah positif, sehingga undefined harus memenuhi

table attributes columnalign right center left columnspacing 0px end attributes row D less than 0 row cell open parentheses negative 12 close parentheses squared minus 4 open parentheses 1 close parentheses open parentheses 2 c plus 15 close parentheses end cell less than 0 row cell 144 minus 8 c minus 60 end cell less than 0 row cell negative 8 c end cell less than cell negative 84 end cell row c greater than cell 84 over 8 end cell row c greater than cell 21 over 2 end cell end table 

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

4

Iklan

Gold Icon

Klaim Gold gratis sekarang!

Dengan Gold kamu bisa tanya soal ke Forum sepuasnya, lho.

Iklan

Ruangguru

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Download di Google Play

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Bantuan & Panduan

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02130930000

02130930000

Ikuti Kami

©2025 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia