I know this may sound peculiar, but I was wondering if any mathematicians have found a method to finding roots purely through calculus without iteration. I can't imagine that such a method exists for all the roots of a polynomial, but I can imagine we can find a couple of roots given that they are either stationary points or points of inflection which can quite easily be found having once found the stationary points and points of inflection. However, beyond this, I can't possibly imagine there exists method to determine roots which are not stationary points or points if inflection. So, my question is: are there methods to find the a particular root of a polynomial, where the particular root is not a stationary point or point of inflection, purely through calculus and not iteration, including iterations using calculus (e.g. Newton's method)?
2026-04-30 02:19:03.1777515543
Is it possible to find solutions to polynomials purely by calculus and without iteration?
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