Polynomial equations are important because they are useful in a wide variety of fields, including biology, economics, cryptography, chemistry, coding and advanced mathematical fields, such as numerical analysis, explains the Department of Biochemistry and Molecular Biophysics at The University of Arizona. Engineers in different fields, such as control engineers, often use polynomial and differential equations to design products that must respond to different sets of stimuli from the user.
The branch of mathematics that deals with polynomials covers an enormous array of different equations and equation types. Polynomials that deal primarily with real numbers can be used in computer programming and developing ciphers for encoding messages.
When imaginary numbers and solutions are used with polynomial equations, they can be used to model more complex system behaviors and reactions. For example, the stability or instability of many systems can be determined through imaginary polynomial equations by engineers. They are also used in the pharmaceutical industry when determining scales of production and ensuring the correct amount of all chemical components make it into every dosage of medication.
Ultimately, polynomial equations are some of the best-equipped to model physical and real-world phenomena. These situations may vary on a case-by-case basis, but the utility of polynomial functions for modeling remains. When developed properly, polynomial modeling functions can be used to solve questions about complex biological and behavioral concepts.