Pertanyaan

Akar-akar persamaan kuadrat x 2 + 2 a x − ( a + 3 ) = 0 adalah α dan β . Jika α 2 + β 2 = 26 , maka nilai a =

Akar-akar persamaan kuadrat $x^{2} + 2 a x - (a + 3) = 0$ adalah $α dan β$ . Jika $α^{2} + β^{2} = 26$ , maka nilai $a =$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Jadi, jawaban yang tepat adalah A.

$begin mathsize 14px style x squared plus 2 a x minus left parenthesis a plus 3 right parenthesis equals 0 alpha squared plus beta squared equals 26 alpha plus beta equals fraction numerator negative b over denominator a end fraction equals fraction numerator negative 2 a over denominator 1 end fraction equals negative 2 a alpha times beta equals c over a equals fraction numerator negative a minus 3 over denominator 1 end fraction equals negative a minus 3 end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell alpha squared plus beta squared end cell equals cell open parentheses alpha plus beta close parentheses squared minus 2 alpha beta end cell row 26 equals cell open parentheses negative 2 a close parentheses squared minus 2 open parentheses negative a minus 3 close parentheses end cell row 26 equals cell 4 a squared plus 2 a plus 6 end cell row 0 equals cell 4 a squared plus 2 a minus 20 end cell row 0 equals cell 2 a squared plus a minus 10 end cell row 0 equals cell open parentheses 2 a plus 5 close parentheses open parentheses a minus 2 close parentheses end cell row cell 2 a plus 5 end cell equals cell 0 space space space space space atau space space a minus 2 equals 0 end cell row cell 2 a end cell equals cell negative 5 space space space space space space space space space space space space space space space space a equals 2 end cell row a equals cell fraction numerator negative 5 over denominator 2 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah A.