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Homework Help: Best ways in solving cubic equations without information on roots

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data

    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:

    2. Relevant equations

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

    3. 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: May 6, 2017
  2. jcsd
  3. Oct 5, 2012 #2


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    Homework Helper

    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.
  4. Oct 9, 2012 #3


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    Science Advisor

    In fact, doing that, it is easy to find three small integer roots.
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