Given the cubic equation: For the general cubic equation (1) with real coefficients, the general formula for the roots, in terms of the coefficients, is as follows if $(2 b^3-9 a b c+27 a^2 d)^2-4 …

How do we derive the so called cubic formula without using Cardano's method or substitution? I would like to see a step by step proof of where wolfram alpha derives this answer. And also …

2021年9月21日 · Formula for the roots of a cubic equation. Ask Question Asked 3 years, 2 months ago. Modified 3 years, 2 ...

2017年7月25日 · $\begingroup$ Journey Through Genius has a very nice section on solving the cubic equation if you are interested in picking up a book on the matter. $\endgroup$ – …

2020年8月12日 · But the proof of derivation of the formula mentioned above was only limited to 1 root. In addition, that formula had no complex conjugates. However as we know, there must be …

So my question is like quadratic formula, is there exist any thing like cubic formula which help in solving cubic equations? For example, I have an equation $$2x^3+9x^2+9x-7=0\tag{1}$$ and I …

2025年1月26日 · Consider the following cubic equation $$x^3-3x^2-x=\sqrt 2$$. Almost all possible solutions are based on the assumption $x=m+n\sqrt 2$, based on the fact $x=\sqrt …

2014年6月8日 · $\begingroup$ Finding eigenvalues of a $3\times 3$ matrix in general requires solving a cubic equation. This kind of problem is very common in teaching, but mysteriously …

2010年7月28日 · Wikipedia's article on quartic functions has a lengthy process by which to get the solutions, but does not give an explicit formula. Beware that in the cubic and quartic formulas, …

2017年6月6日 · About Cardano's formula and the cubic equation. Ask Question Asked 7 years, 8 months ago.