若a,b為整數,且x²-x-1為ax³+bx²+1的因式,則b的值為何?
回答 (1)
2015-11-18 2:48 pm
✔ 最佳答案
當 ax³ + bx² + 1 除以 x² - x - 1 時，商數必為 ax - 1考慮 ax³ + bx² + 1 = (x² - x - 1) (ax - 1) = ax³ - (a + 1)x² - (a - 1)x + 1
∵ x 的係數 = 0
- (a - 1) = 0
a = 1
∴ b = - (a + 1) = - (1 + 1) = -2
收錄日期: 2021-04-18 14:04:12
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