Roboguru

Hasil kali semua akar real dari persamaan:   Adalah ....

Pertanyaan

Hasil kali semua akar real dari persamaan:

begin mathsize 14px style 2 straight x squared plus 3 straight x plus 4 equals 2 square root of 2 straight x squared plus 3 straight x plus 12 end root end style 

Adalah ....

Pembahasan Soal:

Dengan menerapkan konsep persamaan kuadrat:

undefined 

Misalkan: begin mathsize 14px style straight p equals 2 straight x squared plus 3 straight x plus 4 end style, maka:

Error converting from MathML to accessible text. 

Untuk nilai begin mathsize 14px style straight p equals 8 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight x squared plus 3 straight x plus 4 end cell equals 8 row cell 2 straight x squared plus 3 straight x minus 4 end cell equals 0 row straight D equals cell straight b squared minus 4 times straight a times straight c end cell row blank equals cell 3 squared minus 4 times left parenthesis 2 right parenthesis times left parenthesis negative 4 right parenthesis end cell row blank equals cell 9 plus 32 end cell row blank equals 41 row cell straight X subscript 1 times straight X subscript 2 end cell equals cell straight c over straight a end cell row blank equals cell fraction numerator negative 4 over denominator 2 end fraction end cell row blank equals cell negative 2 end cell end table end style  

Untuk nilai Error converting from MathML to accessible text., maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight x squared plus 3 straight x plus 4 end cell equals cell negative 4 end cell row cell 2 straight x squared plus 3 straight x plus 8 end cell equals 0 row cell straight x subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative straight b plus-or-minus square root of straight D over denominator 2 times straight a end fraction end cell row straight D equals cell straight b squared minus 4 times straight a times straight c end cell row blank equals cell 3 squared minus 4 times left parenthesis 2 right parenthesis times left parenthesis 8 right parenthesis end cell row blank equals cell 9 minus 64 end cell row blank equals cell negative 55 end cell end table end style 

Karena nilai begin mathsize 14px style straight D less than negative 1 end style maka tidak ada nilai begin mathsize 14px style x element of R end style yang memenuhi jika Error converting from MathML to accessible text..

Jadi, hasil kali semua akar real dari persamaan begin mathsize 14px style 2 straight x squared plus 3 straight x plus 4 equals 2 square root of 2 straight x squared plus 3 straight x plus 12 end root end style adalah: begin mathsize 14px style negative 2 end style.

 

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 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