A monic polynomial of degree N has N number of coefficients. The product of N number of linear factors has N number of free terms. A complex number has 2 DOF. Therefore, both a monic polynomial and the product of free terms have 2N number of DOF of real values. Thus, it must be possible to have a monic polynomial to be resolved into a set of roots whose cardinality is the degree of the polynomial.
What is wrong with this statement?
What is wrong with this statement?