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Akar-akar persamaan x2+(a−1)x+2=0 adalah α dan β. Jika α=2β  dan a>0 maka nilai a = ...

Pertanyaan

Akar-akar persamaan x squared plus left parenthesis a minus 1 right parenthesis x plus 2 equals 0 space a d a l a h space alpha space d a n space beta. space J i k a space alpha equals 2 beta space dan a>0 maka nilai a = ...

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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

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Jika x1​ dan x2​ adalah akar-akar persamaan kuadrat x2+mx+n=0 dengan x1​+x2​=4 dan x1​x2​=2, maka nilai x1​−x2​ adalah ....

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