大门|大门-CS-2000 |问题49

多项式p（x）满足以下条件：

p(1) = p(3) = p(5) = 1 
p(2) = p(4) = -1 

这样一个多项式的最小次数是 （A） 1. （B） 2. （C） 3. （D） 4. 答复: （D） 说明：

p(1) = p(3) = p(5) = 1 
p(2) = p(4) = -1 

The polynomial touches 0 at least once from 1 to 2, so there
is a root between 1 to 2

The polynomial touches 0 at least once from 2 to 3, so there
is a root between 2 to 3

Similarly, there is at least one root from 3 to 4 and 4 to 5.

So minimum degree is 4.

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