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Throughout time various human activities required some type of mathematical result or solution. For example, agriculture requires the land and size of the crop be measured for tax collection and trade or commerce reasons. When people first took to the seas, the problem of determining the position of a ship arose. With ships came cannons, which brought along problems involving distance, trajectory, and height. To build bridges, roads, and buildings, solutions to problems were needed. Nature was also abundant with questions just waiting to be answered. These questions typically involved things like motion, velocity, acceleration, and time. Today statistics are kept on practically everything. All of these things have some type of mathematical equation related to them. Many of these can be written as polynomial equations. This is desirable, since polynomial equations are considered to be "nicer" than many other types of equations. Much work on solving polynomial equations produced a number of related theorems and observations, in particular, the fundamental theorem of algebra and Descartes's rule of signs.

Fundamental Theorem of Algebra
Descartes's Rule of Signs