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Homework Help: Basic algebra question

  1. Apr 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Not sure how to factor this equation:

    x^4-x^3-x^2+4=0
    btw , I do not have a TI 83 calculator
     
  2. jcsd
  3. Apr 12, 2008 #2
    lol this isnt a simple equation to factor its a 4 exponent polynomial, good luck with that, but there is a method i learn in college, dont remember though
     
  4. Apr 12, 2008 #3
    I'd be curious to know this as well; if I had to guess I’d say that is has no factors given that the graph never crosses the x-axis. I dunno =(
     
  5. Apr 13, 2008 #4
    observe the degradation in powers carefully...
     
  6. Apr 13, 2008 #5
    It doesnt have any real factors, since:
    [tex]x^4-x^3-x^2+4=(x^2-\frac{x}{2}-\frac{6}{8})^2+~(\frac{x}{2}-\frac{6}{8})^2+\frac{184}{64} > 0[/tex]
    :)
     
  7. Apr 13, 2008 #6

    tiny-tim

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    But every real quartic equation has real quadratic factors (because the complex roots come in conjugate pairs):

    (x² + ax + b)(x² + cx + d) :smile:
     
  8. Apr 13, 2008 #7
    uhm didnt know that! but i mistyped a little, i meant real roots, not real factors.
     
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