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Persamaan kuadrat x2−(c−2)x+4=0 mempunyai akar-akar x1​ dan x2​. Jika x1​>1 dan x2​>1, maka ....

Pertanyaan

Persamaan kuadrat x squared minus left parenthesis c minus 2 right parenthesis x plus 4 equals 0 mempunyai akar-akar x subscript 1 dan x subscript 2. Jika x subscript 1 greater than 1 dan x subscript 2 greater than 1, maka ....

  1. c greater than 7

  2. c greater or equal than negative 2

  3. 6 less or equal than c less than 7

  4. c less or equal than negative 2 space atau space c greater or equal than 6

  5. c less or equal than negative 2 space atau space 2 less or equal than c less than 7

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell a x squared plus b x plus c end cell equals 0 row cell x subscript 1 plus x subscript 2 end cell equals cell fraction numerator negative b over denominator a end fraction end cell row cell x subscript 1 times x subscript 2 end cell equals cell c over a end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus left parenthesis c minus 2 right parenthesis x plus 4 end cell equals 0 row blank blank blank row cell x subscript 1 plus x subscript 2 end cell equals cell fraction numerator negative left parenthesis negative left parenthesis c minus 2 right parenthesis right parenthesis over denominator 1 end fraction equals c minus 2 end cell row cell x subscript 1 times x subscript 2 end cell equals cell 4 over 1 equals 4 end cell row blank blank blank row cell x subscript 1 end cell greater than cell 1 rightwards arrow x subscript 1 minus 1 greater than 0 end cell row cell x subscript 2 end cell greater than cell 1 rightwards arrow x subscript 2 minus 1 greater than 0 end cell end table

Jadi,

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight i right parenthesis. space space space space space space space space left parenthesis x subscript 1 minus 1 right parenthesis left parenthesis x subscript 2 minus 1 right parenthesis end cell greater than 0 row cell x subscript 1 times x subscript 2 minus left parenthesis x subscript 1 plus x subscript 2 right parenthesis plus 1 end cell greater than 0 row cell 4 minus left parenthesis c minus 2 right parenthesis plus 1 end cell greater than 0 row c less than 7 row blank blank blank row cell left parenthesis ii right parenthesis. space space space space left parenthesis x subscript 1 minus 1 right parenthesis plus left parenthesis x subscript 2 minus 1 right parenthesis end cell greater than 0 row cell left parenthesis x subscript 1 plus x subscript 2 right parenthesis minus 2 end cell greater than 0 row cell c minus 2 minus 2 end cell greater than 0 row c greater than 4 row cell left parenthesis iii right parenthesis. space space space space space space space space space space space space space space space space space space space space space space space space space space space D end cell greater or equal than 0 row cell left parenthesis c minus 2 right parenthesis squared minus 4 times 1 times 4 end cell greater or equal than 0 row cell c squared minus 4 c minus 12 end cell greater or equal than 0 row cell left parenthesis c minus 6 right parenthesis left parenthesis c plus 2 right parenthesis end cell greater or equal than 0 end table

Dari (i), (ii), dan (iii) diperoleh 6 less or equal than c less than 7.

Oleh karena itu, jawaban yang benar adalah C.

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Misalkan x1​ dan x2​ adalah akar-akar persamaan kuadrat x2+3x−8=0. Nilai x12​+x22​ adalah ....

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