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Pertanyaan

Jika alpha space d a n space beta adalah akar-akar persamaan x squared minus 2 x minus 4 equals 0. Persamaan kuadrat yang akar-akarnya alpha over beta space d a n space beta over alpha adalah ...

  1. x squared minus 3 x minus 1 equals 0

  2. x squared plus 3 x plus 1 equals 0

  3. x squared plus 3 x minus 1 equals 0

  4. x squared minus x plus 1 equals 0

  5. x squared minus 4 x minus 1 equals 0

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

x squared minus 2 x minus 4 equals 0  alpha plus beta equals negative b over a equals 2  alpha beta equals c over a equals negative 4

Persamaan yang akar-akarnya alpha over beta space d a n space beta over alpha

alpha over beta plus fraction numerator begin display style beta end style over denominator begin display style alpha end style end fraction equals fraction numerator begin display style alpha squared plus beta squared end style over denominator begin display style alpha beta end style end fraction equals fraction numerator left parenthesis alpha plus beta right parenthesis squared minus 2 alpha beta over denominator alpha beta end fraction  space space space space space space space space space space space space space equals fraction numerator 2 squared minus 2 left parenthesis negative 4 right parenthesis over denominator negative 4 end fraction equals fraction numerator 4 plus 8 over denominator negative 4 end fraction equals negative 3  alpha over beta x beta over alpha equals fraction numerator alpha beta over denominator alpha beta end fraction equals 1

Persamaan:

x squared minus open parentheses alpha over beta plus beta over alpha close parentheses x plus open parentheses alpha over beta x beta over alpha close parentheses equals 0  x squared minus left parenthesis negative 3 right parenthesis plus 1 equals 0  x squared plus 3 x plus 1 equals 0

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Akar-akar persamaan kuadrat 3x2−x−4=0 adalah x1​ dan x2​. Persarnaan kuadrat baru yang akar-akamya (3x1​−1) dan (3x2​−1) adalah ....

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