The Fundamental Theorem of Algebra states that any polynomial of degree n greater than 0 will have at least one root in the set of complex numbers, and that counting all real, imaginary, and repeated solutions, an nth-degree polynomial will have exactly n solutions. The document further explains that real zeros of a function are its x-intercepts, repeated zeros only touch the x-axis, non-repeated zeros cross the x-axis, and complex roots occur in conjugates.