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Fundamental theorem of algebra

The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero. Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed. The theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division. Despite its name, there is no purely algebraic proof of the theorem, since any proof must use some form of the analytic completeness of the real numbers, which is . Additionally, it is not fundamental for modern algebra; its name was given at a time when algebra was synonymous with theory of equations. (Wikipedia).

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What is the Fundamental theorem of Algebra, really? | Abstract Algebra Math Foundations 217

Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understandin

From playlist Math Foundations

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Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra and some additional notes about how roots of polynomials and complex numbers are related to each other.

From playlist Modern Algebra

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Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

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The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg

In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t

From playlist Algebraic Calculus One

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Calculus: The Fundamental Theorem of Calculus

This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.

From playlist Calculus

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Number Theory - Fundamental Theorem of Arithmetic

Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.

From playlist Proofs

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Calculus - The Fundamental Theorem, Part 3

The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.

From playlist Calculus - The Fundamental Theorem of Calculus

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First Fundamental Theorem of Calculus Calculus 1 AB

I introduce and define the First Fundamental Theorem of Calculus. I finish by working through 4 examples involving Polynomials, Quotients, Radicals, Absolute Value Function, and Trigonometric Functions. Check out http://www.ProfRobBob.com, there you will find my lessons organized by clas

From playlist Calculus

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Fundamental Theorem of Algebra

This math video tutorial provides a basic introduction into the Fundamental Theorem of Algebra which states that a polynomial function of degreen n has exactly n roots provided that n is equal to or greater than 1.

From playlist New Algebra Playlist

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Point-counting and diophantine applications - Jonathan Pila

Hermann Weyl Lectures Topic: Point-counting and diophantine applications Speaker: Jonathan Pila Affiliation: University of Oxford Date: October 23, 2018 For more video please visit http://video.ias.edu

From playlist Hermann Weyl Lectures

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Fundamental theorem of algebra | Polynomial and rational functions | Algebra II | Khan Academy

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra2/polynomial_and_rational/fundamental-theorem-of-algebra/e/the-fundamental-theorem-of-algebra?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII Watch the next lesson: https://www.khanac

From playlist Algebra II | High School Math | Khan Academy

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Cyril Houdayer: Noncommutative ergodic theory of lattices in higher rank simple algebraic groups

Talk by Cyril Houdayer in the Global Noncommutative Geometry Seminar (Americas) on March 18, 2022. https://globalncgseminar.org/talks/tba-28/

From playlist Global Noncommutative Geometry Seminar (Americas)

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Visualizing the Fundamental Theorem of Algebra // Math Minute [#48]

The Fundamental Theorem of Algebra is a statement about the relationship between the number of solutions a polynomial has and the degree of that polynomial. Namely, a polynomial will have the same number of solutions as its degree (once we count something called multiplicities). Subscrib

From playlist Math Minutes

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10% of Algebra Students Get This

TabletClass Math: https://tcmathacademy.com/ A video explaining the fundamental theorem of algebra. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes:

From playlist GED Prep Videos

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My Favorite Theorem: The FUNdamental Theorem of Algebra // Math Minute [#37] [ALGEBRA]

A commenter on a video-sharing platform that will go unnamed asked me about my favorite theorem. Herein, I oblige. Subscribe: http://bit.ly/SubTimRicchuiti | Enable ALL push notifications đź”” I don't know if it's because I'm an 8th grade math teacher, or if it's just because I love polynom

From playlist Math Minutes

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Evaluate the integral with e as the lower bound

👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct

From playlist Evaluate Using The Second Fundamental Theorem of Calculus

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Tropical Geometry - Lecture 5 - Fundamental Theorem | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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