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Homework Help: Any help today would be appreciated, thanks.

  1. Sep 11, 2009 #1
    1. The problem statement, all variables and given/known data
    wtihout using a graphing calc, find the rational roots of P(x) = 2x^4-5x^3+5x^2-5x+3

    2. Relevant equations

    3. The attempt at a solution

    The answers are 1 and 3/2, because this is a homework question. I dont know how they got that though. If anybody can help me today that would be appreciated.

  2. jcsd
  3. Sep 11, 2009 #2


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    Hint: Look up the "rational root theorem":wink:
  4. Sep 11, 2009 #3


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  5. Sep 11, 2009 #4


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    If that isn't clear (thanks, Dick) the rational root theorem says that any rational root of [itex]a_ix^i+ a_{i-1}x^{i-1}+ \cdot\cdot\cdot+ a_1x+ a_0[/itex] must be of the form m/n where m divided [itex]a_i[/itex] and n divides [itex]a_0[/itex] (that's because if x= m/n is root then (x- m/n)= (1/n)(nx- m) must be a factor). Here, [itex]a_n= a_4= 2[/itex] and [itex]a_0= 3[/itex]. Since those are prime, there are not a whole lot of possiblities.
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