 # Carl Friedrich Gauss: The Fundamental Theorem Of Algebra

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The Fundamental Theorem of algebra doesn’t have anything to do with the start of algebra rather it does have something to do with polynomials. It is the theorem of equation solving. It was first proved by Carl Friedrich Gauss (1800) as such the linear factors and irreducible quadratic polynomials are both the building block of all polynomial. The linear factors is the polynomials of degree 1 .The Fundamental Theorem of Algebra tells us when we have factored a polynomial completely. A polynomial has been completely factored only if all of its factors are linear or irreducible quadratic. Whenever polynomial are factored into only linear and irreducible quadratics, it has been factored completely since it can’t be factored further over real numbers. For example, when we have n degree polynomials as such function below: p(x) = axn + bxn-1 + ……k The Fundamental Theorem of Algebra will tell us that this n degree polynomials are going to have n-roots or in other way of seeing it, the n value of x will make the expression on the right to be equal to 0. 2. History of root finding The history of root finding dates back during the Islamic Golden Age. The use of the word “root” originates from an Arabic mathematician called Al-Khwarizmi who is also coined the word “algebra” during writing his first algebra book. The root findings were started when he realize the variable as the root of which an equation grows. By solving the equation, we could find the roots. It is specifically