Oct 11, 2018 · A depressed cubic equation is a cubic with the second degree term missing. (i.e. b=0) Every cubic equation can be transformed into a depressed cubic using the substitution in d).

Mar 26, 2023 · First of all I wanted to clarify that this is my first post here. I was trying to find a solution to the general depressed cubic polynomial and was able to get to the right formula but there are some

Jul 5, 2020 · Note that, if a polynomial has a complex root, then its complex conjugate is also a root. Hence, complex roots always come in pairs. Therefore, any cubic will have either $1$ real and $2$ …

Oct 18, 2024 · This explains geometrically why every cubic can be depressed: every cubic can be shifted so that its inflection point is on the y y -axis, but by the argument above that amounts to …

Discriminant of the depressed cubic Ask Question Asked 9 years ago Modified 5 years, 8 months ago

Jun 11, 2017 · Solving depressed cubic: extra solutions? Ask Question Asked 8 years, 8 months ago Modified 8 years, 8 months ago

Jul 20, 2016 · The depressed cubic equation is a cubic equation of the form $x^3+px+q=0$. This expression sounds strange especially for someone that English is not his mother tongue.

May 8, 2016 · Simplifying the result formula for depressed Cubic Ask Question Asked 9 years, 10 months ago Modified 9 years, 10 months ago

Apr 6, 2025 · Your answer makes it clear why a depressed cubic with rational coefficients and a root of the form $\cos (\theta)$ must yield some variation on $\pi/6$ or $\pi/9$, but while translating a …

Feb 13, 2022 · It is well-known that the roots of a cubic equation can be determined by the Cardano formula. For a survey see my answer to Is there really analytic solution to cubic equation?