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I have an equation, say x^3 - 4*x^2 + 2, so a=1, b=-4, c=0, d=2.

Is there an easy way to express the largest root of such an equation? In this case, the roots are:

3.8661982625090223

-0.65544238154983

0.7892441190408067

But I am trying to find an easier way to extract that 3.866 root in such a way that I can express it in terms of as many digits as I want (incrementally, so as to not waste computer memory doing crazy float math). I've tried looking at the wiki entries for cubic functions and Taylor expansions but I feel like I'm hitting a brick wall.

Apologies if my question is not clear.