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Perturbed function

by sprinkle
Tags: function, perturbed
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sprinkle
#1
Nov20-09, 04:03 PM
P: 3
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
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lurflurf
#2
Nov20-09, 04:53 PM
HW Helper
P: 2,263
Quote Quote by sprinkle View Post
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
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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