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f(x) = 7x² - (a + 13)x + (a² - a - 2)为开口向上的抛物线,要有两个实根,则判别式 = (a + 13)² - 28(a² - a - 2) = -9(3a² - 6a - 25) > 0
3a² - 6a - 25 < 0
(3 - 2√21)/3 < a < (3 + 2√21)/3 (二者分别略小于-2和略大于4) (1)
两个实根分别在(0,1),(1,2),则下列条件同时满足:
(2) f(0) = a² - a - 2 = (a + 1)(a - 2) > 0,a < -1或a > 2 (2)
(3) f(1) = 7 - (a + 13) + a² - a - 2 = a² - 2a - 8 = (a + 2)(a - 4) < 0,-2 < a < 4 (3)
(4) f(2) = 28 - 2(a + 13) + a² - a - 2 = a² - 3a = a(a - 3) > 0,a < 0或a > 3 (4)
四者结合得 - 2 < a < -1或 3 < a < 4
1年前
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