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# Cubic equation

Solution of cubic equation using Vieta's formulae. Created by user request This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1122/. Also, please do not modify any references to the original work (if any) contained in this content.

The canonical form of cubic equation is

Vieta's formulae are used to solve equations as

thus, first step is to divide all coefficients by "a".

Here is calculator, description of calculation using Vieta's formulae are below #### Cubic Equation

Digits after the decimal point: 2
x1

x2

x3

Q

R

S

The only place I was able to find Vieta's formulae tailored for cubic equations is here

First we calculate

Then

If S > 0, then

and we have three real roots:

If S < 0, trigonometric functions are replaced with hyperbolic. Depending on sign of Q

Q > 0:

(real root)

(two complex roots)

Q < 0:

(real root)

(two complex roots)

If S = 0, then it is singular equation and has only two roots:

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