Question

How is the degree of a polynomial related to the concept of complex numbers?

Answer 1

The Fundamental Theorem of Algebra states that any constant-coefficient single-variable polynomial of degree n has (counting multiplicity) n complex roots (Real numbers are a subset of Complex numbers).

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Especially for higher-degree polynomials, some roots may not be real. Certainly, if the polynomial has complex coefficients (having an imaginary part), at least one root will be complex (have an imaginary part). That is, the only way you can find the roots is to admit the existence of complex numbers. One simple example is ...

... x^2 +1 = 0