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Diketahui persamaan kuadrat x2+mx+2−2m2=0  mempunyai akar-akar x1​ dan x2​. Jika 2x1​+x2​=2, maka nilai m adalah …

Pertanyaan

Diketahui persamaan kuadrat begin mathsize 14px style straight x squared plus mx plus 2 minus 2 straight m squared equals 0 end style  mempunyai akar-akar undefined dan undefined. Jika begin mathsize 14px style 2 straight x subscript 1 plus straight x subscript 2 equals 2 end style, maka nilai m adalah …

  1. begin mathsize 14px style negative 1 end style 

  2. begin mathsize 14px style negative 2 over 3 end style 

  3. begin mathsize 14px style 2 over 3 end style 

  4. begin mathsize 14px style 1 end style 

  5. begin mathsize 14px style 2 end style 

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah A.

Pembahasan

Jika begin mathsize 14px style ax squared plus bx plus straight c equals 0 end style  memiliki akar-akar undefined dan undefined, maka berlaku :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x subscript 1 plus straight x subscript 2 end cell equals cell negative straight b over straight a end cell row cell straight x subscript 1 straight x subscript 2 end cell equals cell straight c over straight a end cell end table end style 

Sehingga pada persamaan undefined  berlaku:

begin mathsize 14px style straight x subscript 1 plus straight x subscript 2 equals negative straight m end style ... (1)

begin mathsize 14px style straight x subscript 1 straight x subscript 2 equals 2 minus 2 straight m squared end style ... (2)

Dan juga, didapat hasil sebagai berikut.

begin mathsize 14px style 2 straight x subscript 1 plus straight x subscript 2 equals 2 end style 

begin mathsize 14px style straight x subscript 2 equals 2 minus 2 straight x subscript 1 end style ... (3)


Substitusi persamaan (3) ke persamaan (1) :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x subscript 1 plus 2 minus 2 straight x subscript 1 end cell equals cell negative straight m end cell row cell negative straight x subscript 1 end cell equals cell negative straight m minus 2 end cell row cell straight x subscript 1 end cell equals cell straight m plus 2 end cell end table end style 


Substitusi nilai begin mathsize 14px style straight x subscript 1 equals straight m plus 2 end style ke persamaan (3) :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight x subscript 2 end cell equals cell 2 minus 2 open parentheses straight m plus 2 close parentheses end cell row cell straight x subscript 2 end cell equals cell negative 2 straight m minus 2 end cell end table end style 


Substitusikan nilai undefined dan undefined ke persamaan (2) :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight m plus 2 close parentheses open parentheses negative 2 straight m minus 2 close parentheses end cell equals cell 2 minus 2 straight m squared end cell row cell open parentheses straight m plus 2 close parentheses open parentheses negative 2 close parentheses open parentheses straight m plus 1 close parentheses end cell equals cell negative 2 open parentheses straight m squared minus 1 close parentheses end cell row cell open parentheses straight m plus 2 close parentheses open parentheses straight m plus 1 close parentheses end cell equals cell straight m squared minus 1 end cell row cell straight m squared plus 3 straight m plus 2 end cell equals cell straight m squared minus 1 end cell row cell 3 straight m end cell equals cell negative 3 end cell row straight m equals cell negative 1 end cell end table end style 

Jadi, jawabannya adalah A.

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