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Best ways in solving cubic equations without information on roots

  • #1

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 :grumpy:

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 [Broken]

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! :rofl:
 
Last edited by a moderator:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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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
HallsofIvy
Science Advisor
Homework Helper
41,833
955
In fact, doing that, it is easy to find three small integer roots.
 

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