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Akar-akar persamaan  adalah , , , dan . Nilai  adalah ....

Pertanyaan

Akar-akar persamaan begin mathsize 14px style 2 x to the power of 4 plus t x cubed minus 7 x squared plus n x plus 6 equals 0 end style adalah begin mathsize 14px style negative 2 end style, begin mathsize 14px style 1 end style, begin mathsize 14px style alpha end style, dan begin mathsize 14px style beta end style. Nilai begin mathsize 14px style 2 alpha plus 2 beta end style adalah ....

  1. undefined 

  2. begin mathsize 14px style negative 1 end style 

  3. begin mathsize 14px style 0 end style 

  4. begin mathsize 14px style 2 end style 

  5. begin mathsize 14px style 3 end style 

Pembahasan Video:

Pembahasan Soal:

Teorema faktor

Akar-akar persamaan begin mathsize 14px style 2 x to the power of 4 plus t x cubed minus 7 x squared plus n x plus 6 equals 0 end style adalah begin mathsize 14px style negative 2 end style, begin mathsize 14px style 1 end style, begin mathsize 14px style alpha end style, dan begin mathsize 14px style beta end style.

begin mathsize 14px style p left parenthesis negative 2 right parenthesis equals 2 left parenthesis negative 2 right parenthesis to the power of 4 plus t left parenthesis negative 2 right parenthesis cubed minus 7 left parenthesis negative 2 right parenthesis squared plus n left parenthesis negative 2 right parenthesis plus 6 equals 0 left right double arrow 32 minus 8 t minus 28 minus 2 n plus 6 equals 0 left right double arrow negative 8 t minus 2 n equals negative 10 left right double arrow 4 t plus n equals 5 left right double arrow n equals 5 minus 4 t space... left parenthesis 1 right parenthesis end style

begin mathsize 14px style p left parenthesis 1 right parenthesis equals 2 left parenthesis 1 right parenthesis to the power of 4 plus t left parenthesis 1 right parenthesis cubed minus 7 left parenthesis 1 right parenthesis squared plus n left parenthesis 1 right parenthesis plus 6 equals 0 left right double arrow 2 plus t minus 7 plus n plus 6 equals 0 left right double arrow t plus n equals negative 1 left right double arrow n equals negative 1 minus t space... left parenthesis 2 right parenthesis end style

Dari persamaan (1) dan (2) dapat diperoleh:

begin mathsize 14px style 5 minus 4 t equals negative 1 minus t left right double arrow negative 3 t equals negative 6 left right double arrow t equals 2 end style

Susbstitusi begin mathsize 14px style t equals 1 end style ke persamaan (2):

begin mathsize 14px style n equals negative 1 minus t equals negative 1 minus 2 equals negative 3 end style

Polinomial: begin mathsize 14px style 2 x to the power of 4 plus 2 x cubed minus 7 x minus 3 x plus 6 equals 0 end style.

begin mathsize 14px style 2 x to the power of 4 plus 2 x cubed minus 7 x squared minus 3 x plus 6 equals left parenthesis x plus 2 right parenthesis left parenthesis x minus 1 right parenthesis left parenthesis 2 x squared minus 3 right parenthesis end style

begin mathsize 14px style alpha comma space beta end style merupakan akar dari begin mathsize 14px style 2 x squared minus 3 end style, maka:

begin mathsize 14px style alpha plus beta equals negative begin inline style b over a end style equals negative begin inline style 0 over 2 end style equals 0 end style

begin mathsize 14px style 2 alpha plus 2 beta equals 2 left parenthesis alpha plus beta right parenthesis equals 2 left parenthesis 0 right parenthesis equals 0 end style.

Jadi, jawaban yang tepat adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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