多项式 p(x) 满足以下条件:
p(1) = p(3) = p(5) = 1
p(2) = p(4) = -1
这种多项式的最小次数是
(一) 1
(乙) 2
(三) 3
(四) 4答案: (D)
解释:
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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