What does the Fundamental Theorem of Algebra state?

The Fundamental Theorem of Algebra establishes that every non-constant polynomial equation, in the form of ( P(x) = 0 ), has at least one complex root. This is significant because it encompasses not only real roots but also imaginary roots, thereby affirming that the set of complex numbers is sufficient to solve any polynomial equation. The key aspect here is that the polynomial is non-constant; this implies it has a degree of at least one.

Moreover, this theorem assures mathematicians and students that the complex number system is complete in the sense that any polynomial's solutions will be found within this system. For example, a quadratic polynomial (degree 2) could have two complex roots or two real roots, explaining how all possible polynomial behaviors are covered.

In contrast, the other options provided do not correctly represent the essence of what the Fundamental Theorem of Algebra conveys. Only the correct statement covers the fundamental nature of polynomials and their roots comprehensively.