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Polynomial equation with complex answers

  1. Aug 25, 2008 #1
    x4+4x3-7x2-12x+24=0


    Ive been working on this with my brother for a long time and we dont need to find an answer. we just need to reach a point when we can say that the solution is complex. Any ideas? Any nudge in the right direction with be great.


    We tried completing squares, bruteforcing the answer and many other failed attempts
     
  2. jcsd
  3. Aug 26, 2008 #2

    Defennder

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    What do you mean by "the solution is complex"? There are 4 roots to this. If you find the roots using some online calculators (essentially cheating), you'll see that 2 of them are real and other 2 are complex.
     
  4. Aug 26, 2008 #3
    yea but what if i wanted to figure out the answer without a calculator. how would the process be done?
     
  5. Aug 26, 2008 #4

    tiny-tim

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    points of inflection

    Hi axon23! :smile:

    Differentiate twice to find the points of inflection …

    then you should be able to sketch the graph. :smile:
     
  6. Aug 26, 2008 #5
    I'm not sure what you mean by complex solution but it can be shown that there are no rational solutions by the Rational Root Theorem.
     
  7. Aug 27, 2008 #6

    HallsofIvy

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    Set the derivative equal to 0 to find max and min points. Since this even power, if all minimum values are positive, the graph does not cross the x-axis and there are no real roots.
     
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