A question about kernels and commutative rings

[Artusartos]

Homework Statement

Number 3.42 in this link:

http://www.math.wvu.edu/~hjlai/Teaching/Math541-641/Math_541_HW_4_2004.pdf

The part that I don't understand is...Describe ker ϵ in terms of roots of
polynomials. Does this just mean "What is the kernel of ϵ?"

Homework Equations

The Attempt at a Solution

Is my answer correct (I think it's a bit different from the answer in the doc.)...if not, can you tell me why it is wrong?

Ker ϵ = {f(x) in R[x] : ϵ(f(x)) = 0} = \{f(x) \in R[x]: f(x) = 0 +a_1x + a_2x^2+ ... + a_nx^n\}

Thanks in advance

 

[micromass]

Please use the already existing thread.