# Solution of a depressed cubic equation

• PainterGuy
In summary, the conversation revolves around solving the cubic equation x³-2x-5=0, with the real solution being x≈2.0946. The Wikipedia article explains that this is a depressed cubic and in this case 4p³+27q²>0. The speaker also mentions an incorrect solution of x=2.4142 and asks for help in understanding where they went wrong. The moderator points out a potential error with swapping p and q, to which the speaker responds with humor.

#### PainterGuy

Hi,

I was trying to solve the equation x³-2x-5=0. I solved it online and the real solution is x≈2.0946.

The following is an excerpt from the Wikipedia article on cubic equation.

The cubic equation, x³-2x-5=0, is a depressed cubic and in this case 4p³+27q²>0. But the real root of equation comes out to be different, please see below.

The correct real solution is x≈2.0946 therefore the value x=2.4142 is not correct. Where am I going? Could you please help me?

[Moderator's note: Moved from a technical forum and thus no template.]

Last edited by a moderator:
I think you swapped p and q.

Delta2 and PainterGuy
Thank you.

That was really silly!

I'd say Prozac.

archaic said:
I'd say Prozac.

It just needs a hug

I think it's because all the other equations are calling him odd

Last edited by a moderator:
PainterGuy

## 1. What is a depressed cubic equation?

A depressed cubic equation is a type of polynomial equation with a degree of 3, where the coefficient of the second-degree term is equal to 0. It can be written in the form of ax^3 + bx + c = 0, where a, b, and c are constants.

## 2. How is a depressed cubic equation solved?

A depressed cubic equation can be solved using the cubic formula, which involves finding the roots of the equation using complex numbers. Alternatively, it can also be solved using numerical methods such as Newton's method or the bisection method.

## 3. What are the solutions of a depressed cubic equation?

A depressed cubic equation can have either one real root or three real roots, depending on the values of the coefficients. In some cases, it may also have three complex roots. The solutions can be found using the cubic formula or numerical methods.

## 4. What is the significance of solving a depressed cubic equation?

Solving a depressed cubic equation is important in various fields of science and engineering, such as physics, chemistry, and economics. It allows us to find the roots of a polynomial equation and make predictions or solve problems related to the system or process represented by the equation.

## 5. Are there any real-life applications of depressed cubic equations?

Yes, depressed cubic equations have many real-life applications, such as in finding the optimal solution for a cost-benefit analysis, predicting the trajectory of a projectile, and determining the stability of a chemical reaction. They are also used in computer graphics and animation to create smooth curves and surfaces.