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).
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
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
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
Harder Exercises w/ Polynomial Roots
From playlist Further Polynomials
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
Manipulating the Roots of a Quadratic
More resources available at www.misterwootube.com
From playlist Further Polynomials
Polynomial Roots and Coefficients (1 of 5: Relationship between roots and coefficients of cubics)
More resources available at www.misterwootube.com
From playlist Further Polynomials
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
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
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
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
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
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
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
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
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
66 - Multiplicities of eigenvalues
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
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
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
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