# Solving Cubic Polynomials

Although a closed form solution exists for the roots of polynomials of degree ≤ 4, the general formulae for cubics (and quartics) is ugly. Various simplifications can be made; commonly, the cubic $$a_3\,x^3+a_2\,x^2+a_1\,x+a_0$$ is transformed by substituting $$x = t-a_2/3a_3$$, giving Continue reading Solving Cubic Polynomials

# Solving Polynomials

A well known (if not by name) theorem is the Abel–Ruffini theorem, which states that there is no algebraic expression for the roots of polynomials with degree higher than 4.

A not-so-well-known fact is that for any polynomial $$P(x)$$, it is possible to find (with exact arithmetic) a set of ranges each containing exactly one root of $$P(x)$$. One such algorithm is due to James Victor Uspensky in 1948. Continue reading Solving Polynomials

# .com

Hell is freezing over. Or something. This month I've created a twitter and now a blog-type thing here. Welcome to 2006, I know.