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Pertanyaan

Persamaan kuadrat begin mathsize 14px style x squared minus m x plus 4 equals 0 end style memiliki akar-akar undefined dan begin mathsize 14px style b end style. Jika persamaan kuadrat begin mathsize 14px style negative x squared plus 3 x minus 3 n equals 0 end style  memiliki akar-akar fraction numerator size 14px 3 size 14px a over denominator size 14px 2 size 14px b end fraction size 14pxdan fraction numerator size 14px 3 size 14px b over denominator size 14px 2 size 14px a end fraction, maka nilai dari begin mathsize 14px style m times n end style adalah ....

  1. begin mathsize 14px style 4 over 3 end style atau begin mathsize 14px style negative 4 over 3 end style  

  2. undefined atau begin mathsize 14px style negative 4 end style 

  3. undefined atau undefined 

  4. begin mathsize 14px style negative 3 over 4 end style  

  5. begin mathsize 14px style 3 over 4 end style  

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Diketahui persamaan kuadrat undefined  memiliki akar-akar undefined dan begin mathsize 14px style b end style, maka

 undefined   

Selanjutnya, diketahui persamaan kuadrat undefined  memiliki akar-akar begin mathsize 14px style fraction numerator 3 a over denominator 2 b end fraction end style  dan begin mathsize 14px style fraction numerator 3 b over denominator 2 a end fraction end style, maka

  undefined    

Perhatikan bahwa saat begin mathsize 14px style fraction numerator 3 a over denominator 2 b end fraction plus fraction numerator 3 b over denominator 2 a end fraction equals 3 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 a over denominator 2 b end fraction plus fraction numerator 3 b over denominator 2 a end fraction end cell equals 3 row cell fraction numerator 6 a squared plus 6 b squared over denominator 4 a b end fraction end cell equals 3 row cell fraction numerator 6 left parenthesis a squared plus b squared right parenthesis over denominator 4 a b end fraction end cell equals 3 row cell fraction numerator 6 left parenthesis open parentheses a plus b close parentheses squared minus 2 a b right parenthesis over denominator 4 a b end fraction end cell equals 3 row cell fraction numerator 6 left parenthesis open parentheses m close parentheses squared minus 2 open parentheses 4 close parentheses right parenthesis over denominator 4 left parenthesis 4 right parenthesis end fraction end cell equals 3 row cell fraction numerator 6 left parenthesis m squared minus 8 right parenthesis over denominator 16 end fraction end cell equals 3 row cell fraction numerator 6 m squared minus 48 over denominator 16 end fraction end cell equals 3 row cell 6 m squared minus 48 end cell equals 48 row cell 6 m squared end cell equals 96 row cell fraction numerator 6 m squared over denominator 6 end fraction end cell equals cell 96 over 6 end cell row cell m squared end cell equals 16 row m equals cell plus-or-minus square root of 16 end cell row m equals cell plus-or-minus 4 end cell end table end style 

dan saatbegin mathsize 14px style space open parentheses fraction numerator 3 a over denominator 2 b end fraction close parentheses open parentheses fraction numerator 3 b over denominator 2 a end fraction close parentheses equals 3 n end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 3 a over denominator 2 b end fraction close parentheses open parentheses fraction numerator 3 b over denominator 2 a end fraction close parentheses end cell equals cell 3 n end cell row cell fraction numerator 9 a b over denominator 4 a b end fraction end cell equals cell 3 n end cell row cell 9 over 4 end cell equals cell 3 n end cell row n equals cell 9 over 12 end cell row n equals cell 3 over 4 end cell end table end style  

Jika begin mathsize 14px style m equals 4 end style, maka  undefined.     

Jika begin mathsize 14px style m equals negative 4 end style, maka  begin mathsize 14px style m times n equals left parenthesis negative 4 right parenthesis open parentheses 3 over 4 close parentheses equals negative 3 end style.    

Jadi, jawaban yang tepat adalah C.

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