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Real roots of polynomials


Suppose  Pn[x]  is a polynomial of degree n in x.  Its coefficients
are real.  

Question:  What is a good way of determining the real roots of Pn
and their multiplicities?

	Use NSolve and "cast out" the complex roots and Chop any 
	roots with a "too" small imaginary part (in case NSolve 
	inserts spurious imaginary parts). 
In cases where  n  is large and the number of real roots is small 
compared to  n, one can imagine that better methods exist.  I have 
searched MathSource with no real (pun intended) progress.  Possibly 
this is more a math question than a Mathematica question. 

Help is appreciated.


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