EDB — 1SN

[1SN]Given \(a_ 0\ldots a_{n}∈ℂ\) constants, with \(a_ n≠ 0\), and defining \(p(x)=a_ n x^{n} + a_{n-1} x^{n-1} + \dots a_{1} x + a_ 0\), describe all possible solutions \(f\) of

Show that the solution space is a vector space (based on the field \(ℂ\) of complex numbers) of dimension \(n\).

( Hint. Factorize the polynomial and take advantage of previous exercises. ).