Best ways in solving cubic equations without information on roots

In summary, the conversation discusses a method for solving cubic equations without knowledge of any roots, which is found to be time-consuming. The conversation also mentions the use of the Rational Root theorem to find a rational root, which can simplify the solution process. The conversation ends with a suggestion to try finding a rational root first before resorting to the mentioned technique.
  • #1
cheahchungyin
49
0

Homework Statement



Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming

Homework Equations



The equation and attempt is shown in the image below, tell me if its unclear :shy:

The Attempt at a Solution



http://sphotos-a.ak.fbcdn.net/hphotos-ak-prn1/c67.0.403.403/p403x403/60637_450846098287003_1194154338_n.jpg

eventually found out x=7. Then by reducing the equation into a quadratic, I can find the other roots

So are there better ways in solving cubic? maybe some hacking fast ones? :D Appreciate the help! :smile:
 
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  • #2
You should try to find a rational root first using the Rational Root theorem. If you can find one, then you are practically done. Only if there aren't any would I resort to your technique.
 
  • #3
In fact, doing that, it is easy to find three small integer roots.
 

Related to Best ways in solving cubic equations without information on roots

What is a cubic equation?

A cubic equation is a polynomial equation of the form ax3 + bx2 + cx + d = 0, where a, b, c, and d are constants and x is the variable. It is called a cubic equation because the highest power of x is 3.

Why is it difficult to solve cubic equations without information on roots?

Solving cubic equations without any information on the roots can be challenging because it requires finding the roots through trial and error, which can be time-consuming and may not always result in the correct answer. Additionally, cubic equations do not have a general formula for finding the roots, unlike quadratic equations.

What is the best way to solve cubic equations without information on roots?

The best way to solve cubic equations without any information on the roots is by using the Cardano's method. This method involves transforming the cubic equation into a simpler form and then finding the roots using a formula.

Are there any other methods for solving cubic equations without information on roots?

Yes, there are other methods for solving cubic equations without any information on the roots, such as the Newton's method and the De Moivre's formula. However, these methods may not always be as efficient as Cardano's method.

Can cubic equations be solved without using complex numbers?

Yes, cubic equations can be solved without using complex numbers if the equation has real roots. However, if the equation has complex roots, then it is not possible to solve it without using complex numbers.

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