Pertanyaan

Nilai m yang positif yang membuat akar-akar persamaan kuadrat 12 x 2 + m x + 5 = 0 mempunyai perbandingan 2 : 3 adalah...

Nilai $m$ yang positif yang membuat akar-akar persamaan kuadrat $12 x^{2} + m x + 5 = 0$ mempunyai perbandingan $2 : 3$ adalah...

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Persamaan kuadrat Akar-akar persamaan kuadrat mempunyai perbandingan , Maka Cari akar-akarnya, Di dapatkan akar-akar persamaan kuadrat, kemudian cari nilai Karena nilai positif maka . Oleh karena itu, jawaban yang benar adalah B.

Persamaan kuadrat 12 x squared plus m x plus 5 equals 0

table attributes columnalign right center left columnspacing 0px end attributes row cell 12 x squared plus m x plus 5 end cell equals 0 row cell a x squared plus b x plus c end cell equals 0 row a equals 12 row b equals m row c equals 5 end table

Akar-akar persamaan kuadrat mempunyai perbandingan 2 space colon space 3 , Maka

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 over x subscript 2 end cell equals cell 2 over 3 end cell row cell 3 x subscript 1 end cell equals cell 2 x subscript 2 end cell row cell x subscript 2 end cell equals cell 3 over 2 x subscript 1 end cell end table

Cari akar-akarnya,

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 x subscript 2 end cell equals cell c over a end cell row blank equals cell 5 over 12 end cell row blank blank blank row cell x subscript 1 times 3 over 2 x subscript 1 end cell equals cell 5 over 12 end cell row cell 3 over 2 x subscript 1 squared end cell equals cell 5 over 12 end cell row cell x subscript 1 squared end cell equals cell fraction numerator 5 cross times 2 over denominator 12 cross times 3 end fraction end cell row blank equals cell 10 over 36 end cell row cell x subscript 1 end cell equals cell square root of 10 over 36 end root end cell row cell x subscript 1 end cell equals cell square root of 10 over 6 squared end root end cell row cell x subscript 1 end cell equals cell 1 over 6 square root of 10 end cell row blank blank blank row cell x subscript 2 end cell equals cell 3 over 2 x subscript 1 end cell row cell x subscript 2 end cell equals cell 3 over 2 times 1 over 6 square root of 10 end cell row blank equals cell 3 over 12 square root of 10 end cell row blank blank blank row blank blank blank end table$

Di dapatkan akar-akar persamaan kuadrat, kemudian cari nilai

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell fraction numerator negative b over denominator a end fraction end cell row cell 1 over 6 square root of 10 plus 3 over 12 square root of 10 end cell equals cell fraction numerator negative m over denominator 12 end fraction end cell row cell 2 over 12 square root of 10 plus 3 over 12 square root of 10 end cell equals cell fraction numerator negative m over denominator 12 end fraction end cell row cell 2 square root of 10 plus 3 square root of 10 end cell equals cell negative m end cell row cell negative m end cell equals cell 5 square root of 10 end cell row m equals cell negative 5 square root of 10 end cell end table$

Karena nilai positif maka m equals 5 square root of 10 .

Oleh karena itu, jawaban yang benar adalah B.