Polynomials

Geometrical properties of polynomial roots

In mathematics, a univariate polynomial of degree n with real or complex coefficients has n complex roots, if counted with their multiplicities. They form a multiset of n points in the complex plane. This article concerns the geometry of these points, that is the information about their localization in the complex plane that can be deduced from the degree and the coefficients of the polynomial. Some of these geometrical properties are related to a single polynomial, such as upper bounds on the absolute values of the roots, which define a disk containing all roots, or lower bounds on the distance between two roots. Such bounds are widely used for root-finding algorithms for polynomials, either for tuning them, or for computing their computational complexity. Some other properties are probabilistic, such as the expected number of real roots of a random polynomial of degree n with real coefficients, which is less than for n sufficiently large. In this article, a polynomial that is considered is always denoted where are real or complex numbers and ; thus n is the degree of the polynomial. (Wikipedia).

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Polynomials Functions and Their Graphs Part 3

In this video we look at multiplicity and zeros of a polynomial function as well as the intermediate value theorem.

From playlist Polynomial Functions

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Turning Points and X Intercepts of a Polynomial Function

This video introduces how to determine the maximum number of x-intercepts and turns of a polynomial function from the degree of the polynomial function. Examples are shown with graphs. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Determining the Characteristics of Polynomial Functions

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Polynomial Hack: Identify a Polynomial from Just Two Inputs // #SoME2

A polynomial is a mathematical object built from only addition, subtraction, and multiplication. As such, we can express them using only positive integer powers (and, technically, the zero power for constants), and they can be evaluated everywhere. In a single variable, the polynomial can

From playlist Math Minutes

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FIT3.1.2. Roots of Real Polynomials

Field Theory: We now consider roots of real and complex polynomials. We state and prove the Fundamental Theorem of Algebra, and note its consequences for real polynomials. Then we consider the relation between splitting fields, automorphisms, and roots.

From playlist Abstract Algebra

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Manipulating the Roots of a Quadratic

More resources available at www.misterwootube.com

From playlist Further Polynomials

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Ex: Determine the Least Possible Degree of a Polynomial From the Graph

This video explains how to determine the least possible degree of a polynomial based upon the graph of the function by analyzing the intercepts and turns of the graph. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Determining the Characteristics of Polynomial Functions

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Linear Algebra 2i: Polynomials Are Vectors, Too!

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Linear Algebra 4b: Impossible Decomposition with Polynomials

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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67 - More on eigenvalues

Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering

From playlist Algebra 1M

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Towards a Geometric Analogue of Sarnak's Conjecture - Will Sawin

Workshop on Additive Combinatorics and Algebraic Connections Topic: Towards a Geometric Analogue of Sarnak's Conjecture Speaker: Will Sawin Affiliation: Columbia University Date: October 28, 2022 Work of Mark Shusterman and myself has proven an analogue of Chowla's conjecture for polynom

From playlist Mathematics

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Nicholas Katz - Exponential sums and finite groups

Correction: The affiliation of Lei Fu is Tsinghua University. This is joint work with Antonio Rojas Leon and Pham Huu Tiep, where we look for “interesting” finite groups arising as monodromy groups of “simple to remember” families of exponential sums”.

From playlist Conférence « Géométrie arithmétique en l’honneur de Luc Illusie » - 5 mai 2021

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Ex: Find Key Information about a Given Polynomial Function

This video explains how to write a polynomial function in descending order, find the leading coefficient, give the degree, find the maximum number of x-intercepts, and the maximum number of turns. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Determining the Characteristics of Polynomial Functions

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Linear Algebra 2k1: Examples of Linear Combinations

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Frits Beukers: A supercongruence and hypergeometric motive

Abstract : In this lecture I discuss joint work with Eric Delaygue on supercongruences for certain truncated hypergeometric functions. There will also be a discussion of the hypergeometric motives that underlie these congruences. Recording during the meeting "Algebra, Arithmetic and Combi

From playlist Number Theory

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66 - Multiplicities of eigenvalues

Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering

From playlist Algebra 1M

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5. Eigenvalues and Eigenvectors

MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015 View the complete course: http://ocw.mit.edu/10-34F15 Instructor: James Swan Examples were presented to demonstrate how to find eigenvalues and eigenvectors of a matrix and explain their properties. License: Creative

From playlist MIT 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2015

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3. Feedback, Poles, and Fundamental Modes

MIT MIT 6.003 Signals and Systems, Fall 2011 View the complete course: http://ocw.mit.edu/6-003F11 Instructor: Dennis Freeman License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.003 Signals and Systems, Fall 2011

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Pre-Calculus - Rational roots theorem for polynomials

This video covers the rational roots theorem for polynomials. This theorem is important because when finding zeros, it gives us a list of possible rational zeros we can try. http://www.mysecretmathtutor.com

From playlist Pre-Calculus

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Convex function | Samuelson's inequality | Monotonic function | Wilkinson's polynomial | Zero of a function | Convex hull | Complex conjugate root theorem | Mean | Derivative | Graeffe's method | Continuous function | Big O notation | Geometric mean | Computational complexity | Rational number | Companion matrix | Implicit function theorem | Discriminant | Complex plane | Geometric progression | Variance | Hölder's inequality | Binomial coefficient | Mathematics | Mahler measure | Quadratic function | Reflection symmetry | Vieta's formulas | Bit | Descartes' rule of signs | Square-free polynomial | Galois group | Gershgorin circle theorem | Transpose | Natural logarithm | Edmund Landau | Rouché's theorem | Newton's method | Real-root isolation