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Unformatted text preview: 第 1 次讨论课 Exercise 1 设 a, b, c 是三个不同的数,用 x − a, x − b, x − c 除一元多项 式 f (x) 的余式依次为 r, s, t,试求用 g (x) = (x − a)(x − b)(x − c) 除 f (x) 的 余式。 解: 设 f (x) = q (x)g (x) + r(x),则可设 r(x) = a2 x2 + a1 x + a0 , 则 r(a) = f (a) = r,r(b) = f (b) = s,r(c) = f (c) = t。 故有如下方程组: a0 r 1 a a2 1 b b2 a1 = s 1 c c2 a2 t 容易通过这个方程组解出 a0 , a1 , a2 的值,从而得到 r(x)。 Exercise 2 求 p, q, r 之间的关系,使得 x3 + px2 + qx + r 的根成等比 数列。 解 : 设 x3 + px2 + qx + r 的...
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This note was uploaded on 03/25/2010 for the course MATH 40 taught by Professor F.yu during the Spring '05 term at Tsinghua University.

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