How Do You Approximate the Perturbed Root of a Polynomial Function?

[sprinkle]

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

 

[lurflurf]

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