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Is there any algorithm that can be used to find all the possible roots of a polynomial?

For example, I'd like to find all possible roots of the polynomial $x^3 + 3x^2 + 2x + 6$.

If I remember correctly, the possible rational roots of a polynomial are given by all factors of the constant term, divided by all factors of the leading coefficient - is this true, or is it false?

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@TheChaz Now is there an efficient algorithm for finding the irrational roots of a polynomial? – Anderson Green Nov 4 '12 at 2:30
    
Yes --- Newton's Method, which see. – Gerry Myerson Nov 4 '12 at 2:34
    
dichotomy, newton, etc... – user31280 Nov 4 '12 at 2:35
    
@F'OlaYinka Can you explain what "dichotomy" refers to in this context? – Anderson Green Nov 4 '12 at 2:36

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