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I Help solving a Polynomial

  1. Jun 18, 2017 #1
    I need this solved for x:
    y' = 4ax^3 + 3bx^2 + 2cx + d = 0

    This is to say, I need the formula for the "critical points" of a Quartic function.
    Wikipedia says: "The derivative of a quartic function is a cubic function."

    And I found the above derivative here:

    Any help solving it would be great (it is beyond my ability).
  2. jcsd
  3. Jun 18, 2017 #2


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  4. Jun 18, 2017 #3
    No kidding. Tricky is definitely the word for it.

    I've previously read and re-read that whole page already, and unfortunately, I'm clueless with any high-level math. So it would be impossible for me to use the general cubic equation as an example for me to do the same math tricks to the above cubic.

    I typically Google until I find what I need. Meaning, I need a website to say "this is the formula for XYZ" (and the formula need to be in a form that does not have many Greek letters). Otherwise, I keep searching. It all comes down to: Can I convert it to computer code?

    Therefore, any spoon-feeding would be greatly appreciated.
  5. Jun 18, 2017 #4


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    If you have no numbers for ##a,b,c,d## then you're stuck with the giant formula I quoted. There is no easy way in this generality.
  6. Jun 18, 2017 #5
    Looking closer at it. That's just crazy.
    How can a simple derivative explode into something that big?

    I'm just going to "graph" my Quartic's into a data set and then search for highs and lows instead.

    Sorry to waste your time.
    Thanks anyway.
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