Consider the vector space V of all the real polynomials of degree less than or equal to three,  p(x) = ax^3 + b x^2 + c x + d, and consider the linear transformation T: V ------> V given by the derivative, i.e., T( p ) = p' = 3ax^2 + 2 b x + c. Find the eigenvalues and eigenvectors of this transformation.

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