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Akar-akar persamaan kuadrat 3 x 2 − x − 4 = 0 adalah x 1 ​ dan x 2 ​ . Persarnaan kuadrat baru yang akar-akamya ( 3 x 1 ​ − 1 ) dan ( 3 x 2 ​ − 1 ) adalah ....

Akar-akar persamaan kuadrat adalah dan . Persarnaan kuadrat baru yang akar-akamya  dan adalah ....

  1. begin mathsize 14px style straight x squared minus straight x minus 38 equals 0 end style

  2. begin mathsize 14px style straight x squared plus straight x minus 32 equals 0 end style

  3. begin mathsize 14px style straight x squared plus straight x plus 12 equals 0 end style

  4. begin mathsize 14px style straight x squared plus straight x minus 12 equals 0 end style

  5. begin mathsize 14px style straight x squared minus straight x minus 12 equals 0 end style

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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begin mathsize 14px style straight i right parenthesis space Cari space hubungan space akar minus akar space persamaan space kuadrat space colon  space space space Untuk space persamaan space kuadrat space ax squared plus bx plus straight c equals 0 space yang space memiliki  space space space akar minus akar space straight x subscript 1 space dan space straight x subscript 2 comma space maka  space space space straight x subscript 1 plus straight x subscript 2 equals negative straight b over straight a  space space space straight x subscript 1 straight x subscript 2 equals straight c over straight a  space space space Persamaan space kuadrat space 3 straight x squared minus straight x minus 4 equals 0 space dengan space straight a equals 3 comma space straight b equals negative 1 comma space straight c equals negative 4 comma  space space space memiliki space akar minus akar space straight x subscript 1 space end subscript dan space straight x subscript 2 comma space maka  space space space straight x subscript 1 plus straight x subscript 2 equals negative straight b over straight a equals negative fraction numerator open parentheses negative 1 close parentheses over denominator 3 end fraction equals 1 third  space space space straight x subscript 1 straight x subscript 2 equals straight c over straight a equals fraction numerator negative 4 over denominator 3 end fraction equals negative 4 over 3    ii right parenthesis space Misalkan space akar minus akar space persamaan space kuadrat space baru  space space space space Misalkan space persamaan space kuadrat space baru space memiliki space akar minus akar space straight x subscript 3 space end subscript dan space straight x subscript 4 space dengan  space space space space straight x subscript 3 equals 3 straight x subscript 1 minus 1  space space space space straight x subscript 4 equals 3 straight x subscript 2 minus 1    iii right parenthesis space Cari space hubungan space akar minus akar space persamaan space kuadrat space baru  space space space space space straight x subscript 3 plus straight x subscript 4 equals open parentheses 3 straight x subscript 1 minus 1 close parentheses plus open parentheses 3 straight x subscript 2 minus 1 close parentheses equals 3 straight x subscript 1 plus 3 straight x subscript 2 minus 2 equals 3 open parentheses straight x subscript 1 plus straight x subscript 2 close parentheses minus 2  space space space space space equals 3 open parentheses 1 third close parentheses minus 2 equals 1 minus 2 equals negative 1    space space space space space straight x subscript 3 straight x subscript 4 equals open parentheses 3 straight x subscript 1 minus 1 close parentheses open parentheses 3 straight x subscript 2 minus 1 close parentheses equals 9 straight x subscript 1 straight x subscript 2 minus 3 straight x subscript 1 minus 3 straight x subscript 2 plus 1 equals 9 straight x subscript 1 straight x subscript 2 minus 3 open parentheses straight x subscript 1 plus straight x subscript 2 close parentheses plus 1  space space space space space equals 9 open parentheses negative 4 over 3 close parentheses minus 3 open parentheses 1 third close parentheses plus 1 equals negative 12 minus 1 plus 1 equals negative 12    iv right parenthesis space Menyusun space persamaan space kuadrat space baru  space space space space space Persamaan space kuadrat space baru space dengan space akar minus akar space straight x subscript 3 space dan space straight x subscript 4 space berbentuk  space space space space space straight x squared minus open parentheses straight x subscript 3 plus straight x subscript 4 close parentheses straight x plus straight x subscript 3 straight x subscript 4 equals 0  space space space space space straight x squared minus open parentheses negative 1 close parentheses straight x plus open parentheses negative 12 close parentheses equals 0  space space space space space straight x squared plus straight x minus 12 equals 0 end style

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