Abel's impossibility theorem states that there is no algebraic solution to polynomial equations of degree five or higher But Jordan has shown that any algebraic equation can be solved using …

Jul 28, 2010 · 149 There is, in fact, a general formula for solving quartic (4th degree polynomial) equations. As the cubic formula is significantly more complex than the quadratic formula, the …

If in an other example, you can't find a obvious root then remember that every polynomial with odd degree has a real root (thanks to the intermediate value theorem) and there is a method due to …

Because your equation can be rearranged to a polynomial exponential equation over the algebraic numbers, it cannot have solutions that are elementary numbers. Because your …

In any case, if you start with a system of polynomial equations and compute a Groebner basis for the ideal they generate, you get a "maximally triangular" system of equations which is …

Feb 13, 2012 · Most people learn in linear algebra that its possible to calculate the eigenvalues of a matrix by finding the roots of its characteristic polynomial. However, this method is actually …

Dec 2, 2015 · 22 I looked on Wikipedia for a formula for roots of a 5th degree polynomial, but it said that by Abel's theorem it isn't possible. The Abel's theorem states that you can't solve …

Apr 22, 2021 · 3 I have a system of polynomial equations which I need to solve numerically. The one Im currently interested in has around 20 variables and a similar number of equations. All …

How to solve polynomial equations in a field and/or in a ring? Ask Question Asked 14 years, 5 months ago Modified 10 years, 3 months ago

Nov 9, 2014 · 47 I understand that the quadratic equation can solve any second order polynomial. Furthermore, equations exist for polynomials up to fourth order. However, without a graduate …