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I've been working on a program that finds the roots of a variable polynomial.

So far, I've been using the rational zero theorem, but I've only been able to find integer roots using it. So is there an algorithm to find all real zeros of a polynomial?

In searching similar threads, I've found the Jenkins-Traub algorithm. If I understand correctly, it's a popular algorithm for industry standard softwares, but I haven't a clue how to implement it.

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    I hear Newton's algorithm works decently well for some polynomials. – 2017-02-18
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    Implementing a robust root finding algorithm is bound to be a lot of work. use well tested code instead. – 2017-02-18

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