Roboguru

Diketahui akar-akar persamaan kuadrat  adalah  dan . Jika maka nilai  = …

Pertanyaan

Diketahui akar-akar persamaan kuadrat x squared plus p x minus 3 p plus 1 equals 0 adalah x subscript 1 dan x subscript 2. Jika x subscript 1 squared plus x subscript 2 squared equals 5maka nilai p = …

  1. negative 8 space atau space 0

  2. negative 7 space atau space 1

  3.  negative 6 space atau space 2 

  4.  negative 5 space atau space 2  

  5. negative 4 space atau space 3

Pembahasan Soal:

Diketahui persamaan x squared plus p x minus 3 p plus 1 equals 0 memiliki akar-akar x subscript 1 dan x subscript 2x subscript 1 squared plus x subscript 2 squared equals 5, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 squared plus x subscript 2 squared end cell equals cell open parentheses x subscript 1 plus x subscript 2 close parentheses squared minus 2 x subscript 1 x subscript 2 end cell row 5 equals cell open parentheses negative b over a close parentheses squared minus 2 cross times open parentheses c over a close parentheses end cell row 5 equals cell open parentheses negative p over 1 close parentheses squared minus 2 cross times open parentheses fraction numerator negative 3 p plus 1 over denominator 1 end fraction close parentheses end cell row 5 equals cell p squared minus 2 cross times left parenthesis negative 3 p plus 1 right parenthesis end cell row 5 equals cell p squared plus 6 p minus 2 end cell row 0 equals cell p squared plus 6 p minus 2 minus 5 end cell row 0 equals cell p squared plus 6 p minus 7 end cell row 0 equals cell left parenthesis p plus 7 right parenthesis left parenthesis p minus 1 right parenthesis end cell end table

p equals negative 7 space atau space p equals 1  

Jadi, jawaban yang tepat adalah B

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px plus size 14px 3 size 14px x size 14px minus size 14px 2 size 14px equals size 14px 0

 Diketahui: size 14px a size 14px equals size 14px 1 size 14px comma size 14px space size 14px b size 14px equals size 14px 3 size 14px comma size 14px space size 14px c size 14px equals size 14px minus size 14px 2

 size 14px alpha size 14px plus size 14px beta size 14px equals fraction numerator size 14px minus size 14px b over denominator size 14px a end fraction size 14px equals fraction numerator size 14px minus size 14px 3 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 3 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px left parenthesis size 14px minus size 14px 2 size 14px right parenthesis over denominator size 14px 1 end fraction size 14px equals size 14px 2

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals negative 3 over 2 end style 

begin mathsize 14px style alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 left parenthesis alpha. beta right parenthesis equals left parenthesis negative 3 right parenthesis squared minus 2 left parenthesis 2 right parenthesis equals 9 plus 4 equals 13 end style 

 

1

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat undefined

Diketahui: begin mathsize 14px style a equals 1 comma space b equals 1 comma space c equals negative 1 end style

Penyelesaian:

size 14px alpha size 14px plus size 14px beta size 14px equals fraction numerator size 14px minus size 14px b over denominator size 14px a end fraction size 14px equals fraction numerator size 14px minus size 14px 1 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 1 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px 1 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 1 

size 14px 1 over size 14px alpha size 14px plus size 14px 1 over size 14px beta size 14px equals fraction numerator size 14px beta size 14px plus size 14px alpha over denominator size 14px alpha size 14px. size 14px beta end fraction size 14px equals fraction numerator size 14px alpha size 14px plus size 14px beta over denominator size 14px alpha size 14px. size 14px beta end fraction size 14px equals fraction numerator negative 1 over denominator negative 1 end fraction size 14px equals size 14px 1 

size 14px alpha to the power of size 14px 2 size 14px plus size 14px beta to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px alpha size 14px plus size 14px beta size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px alpha size 14px. size 14px beta size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px minus size 14px 1 size 14px right parenthesis size 14px equals size 14px 1 size 14px plus size 14px 2 size 14px equals size 14px 3 

0

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px minus size 14px 3 size 14px x size 14px plus size 14px 1 size 14px equals size 14px 0 

Diketahui: begin mathsize 14px style a equals 1 comma space b equals negative 3 comma space c equals 1 end style  

Penyelesaian:

 begin mathsize 14px style alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 3 right parenthesis over denominator 1 end fraction equals 3 end style 

begin mathsize 14px style alpha. beta equals c over a equals 1 over 1 equals 1 end style 

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals 3 over 1 equals 3 end style 

begin mathsize 14px style alpha squared plus beta squared equals left parenthesis alpha plus beta right parenthesis squared minus 2 left parenthesis alpha. beta right parenthesis equals left parenthesis 3 right parenthesis squared minus 2.1 equals 9 minus 2 equals 7 end style 

0

Roboguru

Diketahui dan adalah akar-akar persamaan kuadrat berikut. Tentukan nilai , , , dan .

Pembahasan Soal:

Persamaan kuadrat size 14px x to the power of size 14px 2 size 14px minus size 14px 5 size 14px x size 14px minus size 14px 7 size 14px equals size 14px 0 

Diketahui: size 14px a size 14px equals size 14px 1 size 14px comma size 14px space size 14px b size 14px equals size 14px minus size 14px 5 size 14px comma size 14px space size 14px c size 14px equals size 14px minus size 14px 7 

 begin mathsize 14px style alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative left parenthesis negative 5 right parenthesis over denominator 1 end fraction equals 5 end style 

size 14px alpha size 14px. size 14px beta size 14px equals size 14px c over size 14px a size 14px equals fraction numerator size 14px minus size 14px 7 over denominator size 14px 1 end fraction size 14px equals size 14px minus size 14px 7 

begin mathsize 14px style 1 over alpha plus 1 over beta equals fraction numerator beta plus alpha over denominator alpha. beta end fraction equals fraction numerator alpha plus beta over denominator alpha. beta end fraction equals fraction numerator 5 over denominator negative 7 end fraction equals negative 5 over 7 end style 

size 14px alpha to the power of size 14px 2 size 14px plus size 14px beta to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px alpha size 14px plus size 14px beta size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px alpha size 14px. size 14px beta size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px 5 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px left parenthesis size 14px minus size 14px 7 size 14px right parenthesis size 14px equals size 14px 25 size 14px plus size 14px 14 size 14px equals size 14px 39 

 

2

Roboguru

Jumlah nilai m yang mengakibatkan persamaan kuadrat mempunyai akar-akar dengan perbandingan 3 : 4 adalah....

Pembahasan Soal:

m x squared minus left parenthesis 3 m plus 1 right parenthesis x plus left parenthesis 2 m plus 2 right parenthesis equals 0  x subscript 1 colon x subscript 2 equals 3 colon 4  x subscript 1 equals 3 over 4 x subscript 2

space space space space x subscript 1 plus x subscript 2 equals fraction numerator 3 m plus 1 over denominator m end fraction  3 over 4 x subscript 2 plus x subscript 2 equals fraction numerator 3 m plus 1 over denominator m end fraction  space space space space space space space space 7 over 4 x subscript 2 equals fraction numerator 3 m plus 1 over denominator m end fraction  space space space space space space space space space space space space x subscript 2 equals fraction numerator 12 m plus 4 over denominator 7 m end fraction

space space space space space space space space space space space space x subscript 1 x subscript 2 equals fraction numerator 2 m plus 2 over denominator m end fraction  space space space space space space 3 over 4 x subscript 2 left parenthesis x subscript 2 right parenthesis equals fraction numerator 2 m plus 2 over denominator m end fraction  space space space space space space space space space space space space space space space x subscript 2 squared equals fraction numerator 8 m plus 8 over denominator 3 end fraction  open parentheses fraction numerator 12 m plus 4 over denominator 7 m end fraction close parentheses squared equals fraction numerator 8 m plus 8 over denominator 3 end fraction

432 m cubed plus 288 m squared plus 48 m equals 432 m cubed plus 392 m squared  40 m cubed plus 104 m squared plus 48 m equals 0  m subscript 1 plus m subscript 2 plus m subscript 3 equals negative 104 over 40 equals 13 over 5

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

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