Encyclopedia Article

# Roots - Research Article from World of Mathematics

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A root of a function f is a number x such that f(x) = 0. The fundamental theorem of algebra states that if f is a polynomial of degree n with complex number coefficients then it has at most n roots. The problem of finding the roots of f has a four thousand year history. The ancient Egyptians (2000 BC) knew how to find the roots of a degree 2 polynomial equation (or quadratic equation) using the quadratic formula. In the 1500s, Girolamo Cardano discovered how to find the roots of any degree 3 polynomial (or cubic equation). Degree 4 polynomials (quartic equations) were soon easy to solve as well. However, Abel proved in 1827 that there is no general formula that can solve a polynomial of degree 5 (quintic equations) or higher. His discovery, in part, led to the development of modern algebra and group theory. Because of Abel's discovery, mathematicians gave up the...