Pertanyaan

Akar-akar persamaan x 2 + ( a − 1 ) x + 2 = 0 a d a l ah α d an β . J ika α = 2 β dan a>0 maka nilai a = ...

Akar-akar persamaan $x^{2} + (a - 1) x + 2 = 0 a d a l ah α d an β . J ika α = 2 β$ dan a>0 maka nilai a = ...

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

$U n t u k space p e r s a m a a n space k u a d r a t space A x squared plus B x plus C equals 0 space 0 y a n g space m e m i l i k i space a k a r minus a k a r space alpha space d a n space beta comma space m a k a alpha plus beta equals negative B over A alpha beta equals C over A P e r s a m a a n space k u a d r a t space x squared plus left parenthesis a minus 1 right parenthesis x plus 2 equals 0 space d e n g a n space A equals 1 comma B equals left parenthesis a minus 1 right parenthesis comma d a n space C equals 2 space m e m i l i k i space a k a r minus a k a r space alpha space d a n space beta space d i m a n a space alpha equals 2 beta comma space m a k a alpha beta equals 2 over 1 left right double arrow 2 beta cross times beta equals 2 left right double arrow 2 beta squared equals 2 left right double arrow beta squared equals 1 left right double arrow beta equals plus-or-minus 1 A m b i l space beta equals 1 alpha plus beta equals negative B over A left right double arrow 2 beta plus beta equals fraction numerator left parenthesis a minus 1 right parenthesis over denominator 1 end fraction left right double arrow 3 beta equals negative fraction numerator left parenthesis a minus 1 right parenthesis over denominator 1 end fraction left right double arrow negative 3 equals negative a plus 1 left right double arrow a equals 4$