# How to solve cube roots question ?

1. Aug 10, 2006

### sunny86

How to solve cube roots question ?
Example :
x^3 - 100x^2 - 7800x + 16300 = 0

I had think long time but still cannot find the way. Besides trial an error, is there anyway to solve this problem ?
thank you.

2. Aug 10, 2006

### WigneRacah

There are numerical methods to get approximate solutions ...

For an exact solution you may find useful this

http://mizar.uwb.edu.pl/JFM/Vol12/polyeq_1.html" [Broken]

Last edited by a moderator: May 2, 2017
3. Aug 10, 2006

### CRGreathouse

4. Aug 11, 2006

### radou

For a given equation $$x^3+ax^2+bx+c=0$$, we can substitute $$x=y-\frac{a}{3}$$, which implies $$y^3+py+q=0$$, where $$p=b-\frac{a^2}{3}$$, and $$q=\frac{2a^3}{17}-\frac{ab}{3}+c$$. After further manipulation, one can retrieve $$x=\sqrt[3]{-\frac{q}{2}+\sqrt{(\frac{q}{2})^2+(\frac{p}{3})^3}}+\sqrt[3]{-\frac{q}{2}-\sqrt{(\frac{q}{2})^2+(\frac{p}{3})^3}}$$, which represents Cardan's formula.

5. Aug 13, 2006

### sunny86

thank guy ~

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