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How to numerically find the least positive root of equation?

What numerical method should I use and with what starting conditions?

I believe I don't have all the roots to be sure, do I?

Although answer to general case would be nice, I would also add that I'm solving quartic equations.

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Roots to quartic equations can be found exactly - check the wikipedia page for details. For more general equations you could probably use Newton's method, but without more details it's difficult to say anything specific. – in_wolframAlpha_we_trust Apr 2 '13 at 10:39
    
WolframAlpha might be a handy tool too. You can get pretty accurate approximations of roots by just typing your equation. – gev Apr 2 '13 at 10:49

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