A Simple Proof of Descartes's Rule of Signs
A Simple Proof of Descartes's Rule of Signs
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DOI：
10.1080/00029890.2004.11920108
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发表时间：
2004-06
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影响因子：
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通讯作者：
Xiaoshen Wang
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文献类型：
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作者：
Xiaoshen Wang
证明我们只考虑Ao>；0和An>；0的情况。其他案件也可以采取类似的处理方式。因为p(O)>；0和p(X)-oc是x-oc，所以很明显，p的图形与正x轴相交偶数次，其中我们不考虑重数来计算交叉点。如果x=a是p的图形接触但不与正x轴交叉的点，则a的重数是偶数。如果该图
Proof We consider only the case when ao > 0 and an > 0. The other cases can be handled similarly. Because p(O) > 0 and p(x) -oc as x -oc, it is clear that the graph of p crosses the positive x-axis an even number of times, where we count crossings without regard to multiplicity. If x = a is a point at which the graph of p touches but does not cross the positive x-axis, then the multiplicity of a is even. If the graph