Multiplicity of roots of polynomials.

[size=100][size=150][br][br][br]1. Create the following functions on the above applet.  [br] a) [math]P\left(x\right)=\left(x+2\right)^1\left(x-1\right)^1\left(x-3\right)^1[/math][br] [br] b) [math]P\left(x\right)=\left(x+2\right)^2\left(x-1\right)^1\left(x-3\right)^2[/math][br] c) [math]P\left(x\right)=\left(x+2\right)^1\left(x-1\right)^3\left(x-3\right)^1[/math][img width=16,height=112]file:///C:/Users/MBELLO~1/AppData/Local/Temp/msohtmlclip1/01/clip_image009.png[/img] [br][br][br]2.  Create your own examples of various multiplicities and explore.     [br] [br] a)  Describe how the graph behaves at a root of multiplicity 1.[br][br] b)  Describe how the graph behaves at a root of multiplicity 2.[br][br] c)  Describe how the graph behaves at a root of multiplicity 3.[br][br][/size][/size][br]