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Perturbed function 
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#1
Nov2009, 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 


#2
Nov2009, 04:53 PM

HW Helper
P: 2,264

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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