Roots of Polynomials
In all we have done so far concerning polynomials, at no moment we had any intent of substituting X by an element of \(\mathbb K\). Even in Theorem 14.10 and Example 14.15, the notation f(z), used to denote the complex number obtained by formally substituting X by z in the expression of \(f\in \mathbb C[X]\), was a mere convention. This is no surprise, for we are looking at polynomials as formal expressions, rather than as functions. In this sense, the indeterminate X is a symbol with no arithmetic meaning, and we have even stressed before that we could have used the symbol \(\square \), instead.