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This section contains 526 words(approx. 2 pages at 300 words per page) |

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...

This section contains 526 words(approx. 2 pages at 300 words per page) |