Apabila m adalah akar x2+3x−1=0, maka nilai dari m3−10m= ...

Pertanyaan

Apabila m adalah akar x squared plus 3 x minus 1 equals 0, maka nilai dari m cubed minus 10 m equals ...

  1. negative 6

  2. negative 4

  3. negative 3

  4. negative 2

  5. 4

A. Acfreelance

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

1. Cari akar-akar dari x squared plus 3 x minus 1 equals 0

Untuk menentukan akar-akar dari persamaan kuadrat a x squared plus b x plus c equals 0 menggunakan rumus abc seperti berikut:

x subscript 1 comma 2 end subscript equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction

Diketahui persamaan x squared plus 3 x minus 1 equals 0:

a equals 1 b equals 3 c equals negative 1

Akar-akarnya adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell m subscript 1 comma 2 end subscript end cell equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative 3 plus-or-minus square root of 3 squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 1 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row blank equals cell fraction numerator negative 3 plus-or-minus square root of 9 plus 4 end root over denominator 2 end fraction end cell row blank equals cell fraction numerator negative 3 plus-or-minus square root of 13 over denominator 2 end fraction end cell end table

Maka, akar-akar dari persamaan x squared plus 3 x minus 1 equals 0 adalah m subscript 1 equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction end cell end table space atau space m subscript 2 equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction end cell end table.

Substitusikan kedua akar ke m cubed minus 10 m.

  • Untuk m subscript 1 equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell m cubed minus 10 m end cell equals cell open parentheses fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction close parentheses cubed minus 10 open parentheses fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 9 minus 6 square root of 13 plus 13 over denominator 4 end fraction close parentheses open parentheses fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction close parentheses minus 5 open parentheses negative 3 plus square root of 13 close parentheses end cell row blank equals cell open parentheses fraction numerator 22 minus 6 square root of 13 over denominator 4 end fraction close parentheses open parentheses fraction numerator negative 3 plus square root of 13 over denominator 2 end fraction close parentheses plus 15 minus 5 square root of 13 end cell row blank equals cell fraction numerator negative 66 plus 40 square root of 13 minus 78 over denominator 8 end fraction plus 15 minus 5 square root of 13 end cell row blank equals cell fraction numerator 40 square root of 13 minus 144 over denominator 8 end fraction plus 15 minus 5 square root of 13 end cell row blank equals cell 5 square root of 13 minus 18 plus 15 minus 5 square root of 13 end cell row blank equals cell negative 3 end cell end table

  • Untuk m subscript 2 equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell m cubed minus 10 m end cell equals cell open parentheses fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction close parentheses cubed minus 10 open parentheses fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 9 plus 6 square root of 13 plus 13 over denominator 4 end fraction close parentheses open parentheses fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction close parentheses minus 5 open parentheses negative 3 minus square root of 13 close parentheses end cell row blank equals cell open parentheses fraction numerator 22 plus 6 square root of 13 over denominator 4 end fraction close parentheses open parentheses fraction numerator negative 3 minus square root of 13 over denominator 2 end fraction close parentheses plus 15 plus 5 square root of 13 end cell row blank equals cell fraction numerator negative 66 minus 40 square root of 13 minus 78 over denominator 8 end fraction plus 15 plus 5 square root of 13 end cell row blank equals cell fraction numerator negative 40 square root of 13 minus 144 over denominator 8 end fraction plus 15 plus 5 square root of 13 end cell row blank equals cell negative 5 square root of 13 minus 18 plus 15 plus 5 square root of 13 end cell row blank equals cell negative 3 end cell end table

Diperoleh nilai m cubed minus 10 m dari kedua akar bernilai sama yaitu negative 3.

Sehingga, nilai dari m cubed minus 10 m adalah negative 3.

Jadi, jawaban yang tepat adalah C.

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