Pertanyaan

Akar-akar persamaan x 2 + ( a − 1 ) x + 2 = 0 adalah α dan β . Jika α = 2 β dan a> 0 maka nilai a =....

Akar-akar persamaan $x^{2} + (a - 1) x + 2 = 0$ adalah α dan β. Jika α = 2β dan a>0 maka nilai a =....

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

$x squared plus left parenthesis a minus 1 right parenthesis x plus 2 equals 0 a equals 1 comma b equals a minus 1 comma c equals 2 alpha equals 2 beta alpha plus beta equals fraction numerator negative b over denominator a end fraction 2 beta plus beta equals fraction numerator negative left parenthesis a minus 1 over denominator 1 end fraction 3 beta equals 1 minus a beta equals fraction numerator 1 minus a over denominator 3 end fraction alpha. beta equals c over a 2 beta. beta equals 2 over 1 2 beta squared equals 2 beta squared equals 1 open parentheses fraction numerator 1 minus a over denominator 3 end fraction close parentheses squared equals 1 fraction numerator 1 minus 2 a plus a squared over denominator 9 end fraction equals 1 1 minus 2 a plus a squared equals 9 a squared minus 2 a minus 8 equals 0 left parenthesis a minus 4 right parenthesis left parenthesis a plus 2 right parenthesis a equals 4 space a t a u space a equals negative 2 k a r e n a space a greater than 0 m a k a space n i l a i space y a n g space m e m e n u h i space y a i t u space a equals 4$