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Is this cublc polynomial function solvable?

  1. Dec 8, 2012 #1
    Here is a very difficult cubic polynomial.

    x^3 - x - 2 = 0

    I am wondering whether it is solvable or not. Please think about it.
     
  2. jcsd
  3. Dec 8, 2012 #2
    I need help with this too I posted a similar one and haven't got a response... mine was x^3 + 9x -1=0...They are solvable, but I don't know how to get an answer algebraically or graphically.
     
  4. Dec 8, 2012 #3
    EDIT: Deleted totally misleading answer. Ignore if you read it.
     
    Last edited: Dec 8, 2012
  5. Dec 8, 2012 #4

    symbolipoint

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    Are they solvable? Let's have a guess: The first one can be tested for divisibility by x+1, x-1, x+2, and x-2. The second one can be tested for divisibility by x+1 and x-1. The results may be faster if you know synthetic division.
     
  6. Dec 8, 2012 #5
    Thank you that's all I needed!
     
  7. Dec 8, 2012 #6

    SteamKing

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    You can use synthetic division, but isn't it simpler to just evaluate the polynomial and see if the equation is satisfied?
     
  8. Dec 9, 2012 #7

    micromass

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  9. Dec 9, 2012 #8

    symbolipoint

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    The first binomial rendering zero remainder is (x-2). The quotient is x^2+2x+1 which is (x+1)^2. No need to use Cardano's or Vietas substitution for this cubic (micromass gave a good reference Wikipedia article).
     
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