![]() ![]() So in these cases we have to resort to numeric linear approximation. ![]() Nonetheless the example is still valid, and demonstrates how would you apply Newton's method, to any polynomial, so let's crack on. Sorry about that, I'm no mathematician by any means. It turns out that this polynomial could be factored into $latex x^2(x-1)(6x^2 + x - 3)$ and solved with traditional cubic formula.Īlso the theorem I referred to is the Abel-Ruffini Theorem and it only applies to the solution to the general polynomial of degree five or greater. Some nice guys pointed out on reddit that I didn't quite get the theory right. What's going on? We all learned the quadratic formula in school, and there are formulas for cubic and quartic polynomials, but Galois proved that no such "root-finding" formula exist for fifth or higher degree polynomials, that uses only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc). Unfortunately we know from the Galois theory that there is no formula for a 5th degree polynomial so we'll have to use numeric methods. Let's say we have a complicated polynomial:Īnd we want to find its roots. We'll code it up in 10 lines of Python in this post. Newton's method, which is an old numerical approximation technique that could be used to find the roots of complex polynomials and any differentiable function. ![]()
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