finding a polynomial with specified zeros寻找一个指定的多项式零点

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1、FindingaPolynomialwithSpecifiedRealZeros:Ifthedegreeofapolynomialfunctionis,itthenhaszeros/roots/solutions/factors.1)Findapolynomialofdegree4thathaszeros-3,0,1and5.2)Findapolynomialofdegree3thathasrootsof1,3and4.3)Findapolynomialofdegree4thathassolutionso

2、f1,3and4.4)Findapolynomialofdegree5thathaszeros0,-3,and-105)Findapolynomialthathasasfactorsandhasadegreeof5.Note:Polynomialhaszerosof-1,0,2withmultiplicities2,4and3.Supposethatisazeroofofmultiplicity:.Thentheshapeofthegraphofnearisasfollows:MultiplicitySh

3、apeofgraphnearthex-interceptorisevenccorisoddccPutmoresimply:**Ifthegraphtouchesthex-axisithasevenmultiplicity**Ifthegraphcrossesthex-axisithasoddmultiplicity6)Findpolynomialwithadegreeof4suchthatithasx-interceptsof3,4and5,where5hasmultiplicityof2.7)Findp

4、olynomialwithdegreeof6suchthatithaszerosof2,-4and0,where2hasmultiplicityof3and-4hasmultiplicityof2.Findthepolynomialofthespecifieddegreewhosegraphisshown:8)Degree39)Degree410)Degree6