Re: [高中] 多項式難題
※ 引述《iddee ()》之銘言：
: 設 f(x) 是三次多項式且滿足
: f(1981) = 1
: f(1982) = 9
: f(1983) = 8
: f(1984) = 5
: 求 f(1985)
也可以用平移來簡化問題，並配合牛頓插值法
命 g(x) = f(x+1981)
則 g(0)=1, g(1)=9, g(2)=8, g(3)=5
則可命 g(x) = ax(x-1)(x-2) + bx(x-1) + cx + 1
可解得 9 = g(1) = c + 1 => c = 8
8 = g(2) = 2b + 17 => b = -9/2
5 = g(3) = 6a - 2 => a = 7/6
f(1985) = g(4) = (7/6)*24 + (-9/2)*12 + 8*4 + 1 = 7.
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