The Quadratic Equation Proposition

In mathematical history, while solutions to linear equations with natural number coefficients necessitated creation of integers and rational numbers, quadratic equations required real and complex numbers that were quite profound in nature. Real numbers, as sections of rational numbers, not only encompassed irrationals, but were also order-complete and, thus, essential for Mathematical Analysis. Complex numbers, as ordered pairs of real numbers, provided solutions to every polynomial equation with complex number coefficients, and, quite remarkably, offered useful mathematical representations, including linking exponential function with trigonometric functions. While Quadratic Equation Proposition provides algebraic expressions with radicals for solving cubic and quartic equations, no such expressions are possible for solving general higher degree polynomials.