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Jika  H={x∣x2−3x−40<0} dan K={x∣x2−x−6≥0} maka H∩K=....

Pertanyaan

Jika  H equals open curly brackets x vertical line x squared minus 3 x minus 40 less than 0 close curly brackets dan K equals open curly brackets x vertical line x squared minus x minus 6 greater or equal than 0 close curly brackets maka H intersection K equals....

  1. open curly brackets x vertical line minus 5 less than x less or equal than negative 2 space atau space 3 less or equal than straight x less than 8 close curly brackets

  2. open curly brackets x vertical line minus 3 less or equal than x less or equal than 2 space atau space 5 less than straight x less than 8 close curly brackets

  3. open curly brackets x vertical line minus 3 less or equal than x less or equal than 0 space atau space 2 less or equal than straight x less than 8 close curly brackets

  4. open curly brackets x vertical line minus 5 less than straight x less than 8 close curly brackets

  5. open curly brackets x vertical line minus 3 less or equal than straight x less or equal than 2 close curly brackets

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Diketahui pertidaksamaan H equals open curly brackets x vertical line x squared minus 3 x minus 40 less than 0 close curly brackets dan K equals open curly brackets x vertical line x squared minus x minus 6 greater or equal than 0 close curly brackets.  Dari pertidaksamaan tersebut diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 3 x minus 40 end cell less than 0 row cell open parentheses x minus 8 close parentheses open parentheses x plus 5 close parentheses end cell less than 0 end table

Dengan demikian, pembuat nol dari pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 3 x minus 40 end cell less than 0 end table adalah x equals 8 atau x equals negative 5.

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus x minus 6 end cell greater or equal than 0 row cell open parentheses x minus 3 close parentheses open parentheses x plus 2 close parentheses end cell greater or equal than 0 end table

 

Dengan demikian, pembuat nol dari pertidaksamaan table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus x minus 6 end cell greater or equal than 0 end table adalah x equals 3 atau x equals negative 2.

Jadi,solusi dari H intersection K adalah 

open curly brackets straight x vertical line minus 5 less than straight x less or equal than negative 2 space atau space 3 less or equal than straight x less than 8 close curly brackets

Jadi, jawaban yang tepat adalah A.

73

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Tentukanlah nilai m supaya persamaan kuadrat x2−2mx+3m=0 mempunyai dua akar real yang berbeda.

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