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Perturbed function

  1. Nov 20, 2009 #1
    Consider the polynomial: f(x)= x^5- 300x^3- 126x+ 5005
    which has a root alpha= 5. Also consider the perturbed function
    F_e(x)= f(x)- epsilon x^5= (1- epsilon)x^5- 300x^3- 126x+ 5005
    where epsilon is a small number. Letting alpha(epsilon) denote the perturbed root of F_e(x)= 0 corresponding to alpha(0)= 5, approximate alpha(epsilon)- 5.

    The problem I'm having is that I don't understand what the question is asking.
    I tried looking at a few perturbed function question but I can't seem to get it
  2. jcsd
  3. Nov 20, 2009 #2


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    Homework Helper

    5 is not a root of that equation, perhaps it should be f(x)= x^5- 300x^2- 126x+ 5005?
    The idea is since the two polynomials are close the roots should be close
    take alpha=5+a epsilon+b epsilon^2+...
    find the coefficients
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