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Diketahui p dan q adalah akar-akar persamaan kuadrat x2+(3a−2)x−6=0. Jika 2p−q=−8, maka nilai a adalah ...

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Diketahui p dan q adalah akar-akar persamaan kuadrat x squared plus open parentheses 3 a minus 2 close parentheses x minus 6 equals 0. Jika undefined, maka nilai undefined adalah undefined 

B. Hary

Master Teacher

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Jawaban

nilai a yang mungkin adalah undefined   

Pembahasan

Diketahui :

Persamaan kuadratundefined x squared plus left parenthesis 3 a minus 2 right parenthesis x minus 6 equals 0. space
begin mathsize 14px style p end style dan begin mathsize 14px style q end style adalah akar-akar persamaan kuadrat  
begin mathsize 14px style 2 p minus q equals negative 8 end style

Ditanya :

Maka nilai begin mathsize 14px style a end style adalah? 

Jawab :

Berdasarkan persamaan kuadrat pada soal, maka :

straight a equals 1 straight b equals left parenthesis 3 straight a minus 2 right parenthesis straight c equals negative 6 

#Penjumlahan akar-akar

table attributes columnalign right center left columnspacing 0px end attributes row cell p plus q end cell equals cell negative b over a end cell row cell p plus q end cell equals cell negative fraction numerator left parenthesis 3 a minus 2 right parenthesis over denominator 1 end fraction end cell row cell p plus q end cell equals cell negative 3 a plus 2 end cell row q equals cell negative 3 a plus 2 minus p space..... space left parenthesis 1 right parenthesis end cell end table    

#Perkalian akar-akar

begin mathsize 14px style p q equals c over a p q equals fraction numerator negative 6 over denominator 1 end fraction p q equals negative 6 space space q equals negative 6 over p...... space left parenthesis 2 right parenthesis end style   

#Substitusi persamaan (1) ke begin mathsize 14px style bold 2 bold italic p bold minus bold italic q bold equals bold minus bold 8 end style

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p minus q end cell equals cell negative 8 end cell row cell 2 p minus open parentheses negative 3 a plus 2 minus p close parentheses end cell equals 8 row cell 2 p plus 3 a minus 2 plus p end cell equals 8 row cell 3 p plus 3 a end cell equals cell 10 space...... left parenthesis 3 right parenthesis end cell end table 

#Substitusi persamaan (2) ke begin mathsize 14px style bold 2 bold italic p bold minus bold italic q bold equals bold minus bold 8 end style,

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight p minus straight q end cell equals cell negative 8 end cell row cell 2 straight p minus open parentheses negative 6 over straight p close parentheses end cell equals cell negative 8 end cell row cell 2 straight p plus open parentheses 6 over straight p close parentheses end cell equals cell negative 8 space space space space space space open square brackets cross times ke minus 2 space ruas space dengan space straight p close square brackets end cell row cell open parentheses 2 straight p cross times straight p close parentheses plus open parentheses 6 over straight p cross times straight p close parentheses end cell equals cell open parentheses negative 8 cross times straight p close parentheses space end cell row cell 2 straight p squared plus 6 end cell equals cell negative 8 straight p end cell row cell 2 straight p squared plus 8 straight p plus 6 end cell equals 0 row cell left parenthesis 2 p plus 6 right parenthesis left parenthesis p plus 1 right parenthesis end cell equals 0 row cell 2 p plus 6 end cell equals cell 0 space atau space p plus 1 equals 0 end cell row cell 2 p end cell equals cell negative 6 space space space space space space space space space space space p equals negative 1 end cell row p equals cell negative 3 space space space space space space space space space space space space space end cell end table

Substitusi begin mathsize 14px style bold italic p bold equals bold minus bold 3 end style ke persamaan (3)

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 straight p plus 3 straight a end cell equals 10 row cell 3 left parenthesis negative 3 right parenthesis plus 3 straight a end cell equals 10 row cell negative 9 plus 3 straight a end cell equals 10 row cell 3 straight a end cell equals 19 row straight a equals cell 19 over 3 end cell end table   

Substitusi Error converting from MathML to accessible text. ke persamaan (3)

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 p plus 3 a end cell equals 10 row cell 3 open parentheses negative 1 close parentheses plus 3 a end cell equals 10 row cell negative 3 plus 3 a end cell equals 10 row cell 3 a end cell equals 13 row a equals cell 13 over 3 end cell end table 

 

Jadi, nilai a yang mungkin adalah undefined   

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