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The fundamental theorem of algebra, also called d'Alembert's theorem [1] or the d'Alembert–Gauss theorem, [2] states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
German stamp commemorating Gauss's 200th anniversary: the complex plane or Gauss plane. In his doctoral thesis from 1799, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
In 1806 Jean-Robert Argand independently issued a pamphlet on complex numbers and provided a rigorous proof of the fundamental theorem of algebra. [35] Carl Friedrich Gauss had earlier published an essentially topological proof of the theorem in 1797 but expressed his doubts at the time about "the true metaphysics of the square root of −1". [36]
It was the first complete and rigorous proof of the theorem, and was also the first proof to generalize the fundamental theorem of algebra to include polynomials with complex coefficients. The first textbook containing a proof of the theorem was Cauchy's Cours d'analyse de l'École Royale Polytechnique (1821). It contained Argand's proof ...
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
In algebra, Gauss's lemma, [1] named after Carl Friedrich Gauss, is a theorem [note 1] about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem of arithmetic). Gauss's lemma underlies all the theory of factorization ...
The Trump administration's rapid dismantling of the U.S. consumer protection watchdog will have broad implications for consumers with credit cards, mortgages and bank accounts, leaving Americans ...
In Disquisitiones Arithmeticae (1801) Gauss proved the unique factorization theorem [1] and used it to prove the law of quadratic reciprocity. [ 2 ] In mathematics , the fundamental theorem of arithmetic , also called the unique factorization theorem and prime factorization theorem , states that every integer greater than 1 can be represented ...