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Pertanyaan

Diketahui alpha dan beta merupakan akar-akar persamaan kuadrat 2 x squared minus 3 x minus 5 equals 0 Persamaan kuadrat yang akar-akarnya open parentheses 2 plus 1 over alpha close parentheses dan open parentheses 2 plus 1 over beta close parentheses adalah .. ..

  1. 5 x squared minus 17 x plus 12 equals 0

  2. 5 x squared plus 17 x plus 12 equals 0

  3. 5 x squared minus 17 x plus 24 equals 0

  4. 5 x squared minus 23 x plus 24 equals 0

  5. 5 x squared plus 23 x plus 24 equals 0

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A

Pembahasan

Diketahui alpha dan beta merupakan akar-akar persamaan kuadrat 2 x squared minus 3 x minus 5 equals 0. Maka persamaan kuadrat yang akar-akarnya open parentheses 2 plus 1 over alpha close parentheses dan open parentheses 2 plus 1 over beta close parentheses adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus left parenthesis x subscript 1 plus x subscript 2 right parenthesis x plus x subscript 1. x subscript 2 end cell equals 0 row cell x squared minus open square brackets open parentheses 2 plus 1 over alpha close parentheses plus open parentheses 2 plus 1 over beta close parentheses close square brackets x plus open parentheses 2 plus 1 over alpha close parentheses open parentheses 2 plus 1 over beta close parentheses end cell equals 0 row cell x squared minus open parentheses 4 plus 1 over alpha plus 1 over beta close parentheses x plus 4 plus 2 over alpha plus 2 over beta plus fraction numerator 1 over denominator alpha beta end fraction end cell equals 0 row cell x squared minus open parentheses 4 plus fraction numerator alpha plus beta over denominator alpha beta end fraction close parentheses x plus 4 plus fraction numerator 2 left parenthesis alpha plus beta right parenthesis over denominator alpha beta end fraction plus fraction numerator 1 over denominator alpha beta end fraction end cell equals 0 row cell x squared minus open parentheses 4 plus fraction numerator begin display style bevelled fraction numerator negative b over denominator a end fraction end style over denominator begin display style bevelled c over a end style end fraction close parentheses x plus 4 plus fraction numerator 2 open parentheses begin display style bevelled fraction numerator negative b over denominator a end fraction end style close parentheses over denominator begin display style bevelled c over a end style end fraction plus fraction numerator 1 over denominator begin display style bevelled c over a end style end fraction end cell equals 0 row cell x squared minus open parentheses 4 plus fraction numerator begin display style bevelled fraction numerator negative left parenthesis negative 3 right parenthesis over denominator 2 end fraction end style over denominator begin display style bevelled fraction numerator negative 5 over denominator 2 end fraction end style end fraction close parentheses x plus 4 plus fraction numerator 2 open parentheses begin display style bevelled fraction numerator negative left parenthesis negative 3 right parenthesis over denominator 2 end fraction end style close parentheses over denominator begin display style bevelled fraction numerator negative 5 over denominator 2 end fraction end style end fraction plus fraction numerator 1 over denominator begin display style bevelled fraction numerator negative 5 over denominator 2 end fraction end style end fraction end cell equals 0 row cell x squared minus open parentheses 4 minus 3 over 5 close parentheses x plus 4 minus 6 over 5 minus 2 over 5 end cell equals 0 row cell 5 x squared minus left parenthesis 20 minus 3 right parenthesis x plus 20 minus 6 minus 2 end cell equals 0 row cell 5 x squared minus 17 x plus 12 end cell equals 0 end table

Jadi, jawaban yang tepat adalah A

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