Fundamental theorem of algebra

The fundamental theorem of algebra states that over the complex numbers every polynomial of degree $n$ has exactly $n$ roots (counted with multiplicity): $\mathbb{C}$ is algebraically closed. From here Vieta’s relations extend to polynomials of any degree and one arrives at Newton’s identities for the power sums of the roots.

• Fundamental theorem of algebra
• Generalised Vieta’s relations
• Newton’s identities for power sums