fundamental theorem of algebra


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fundamental theorem of algebra

[¦fən·də¦ment·əl ¦thir·əm əv ′al·jə·brə]
(mathematics)
Every polynomial of degree n with complex coefficients has exactly n roots counted according to multiplicity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In fulfillment of this standard, he provided the first correct proofs of such landmark results as the fundamental theorem of algebra (a theorem in complex analysis that states essentially that every polynomial equation has a complex root), and the law of quadratic reciprocity, which is concerned with the solvability of certain pairs of quadratic congruences and is crucial to the development of number theory.
The fundamental theorem of algebra was first stated by d'Alembert in 1746 but was only partially proved.
The fundamental theorem of algebra states that every equation of the nth degree has n roots.

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