• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Exam 2 Solutions
Exam 2 Solutions

1999
1999

Quaternions are turning tomb raiders on their heads
Quaternions are turning tomb raiders on their heads

Full text
Full text

Rational Zeros of a Polynomial
Rational Zeros of a Polynomial

... The easiest way to find out which of these possible rational zeros are actual zeros of f (x ) is to use the Remainder Theorem. The Remainder Theorem tells us that if we substitute a number, call it n, into f (x ) , the result will be the same as the remainder when we divide f (x ) by x − n . If n is ...
CORE@TCA SIDE BY SIDE STANDARDS Algebra I/Algebra II
CORE@TCA SIDE BY SIDE STANDARDS Algebra I/Algebra II

2.4 Points on modular curves parameterize elliptic curves with extra
2.4 Points on modular curves parameterize elliptic curves with extra

Slide 1
Slide 1

SPRINGER’S REGULAR ELEMENTS OVER ARBITRARY FIELDS
SPRINGER’S REGULAR ELEMENTS OVER ARBITRARY FIELDS

... This paper generalizes Springer’s theory of regular elements in complex reflection groups, extending it to reflection groups over an arbitrary field whose polynomial invariants form a polynomial algebra. We begin by discussing Springer’s results, and some of our motivation. An element g in GLn (C) o ...
GEOMETRIC CONSTRUCTIONS AND ALGEBRAIC FIELD
GEOMETRIC CONSTRUCTIONS AND ALGEBRAIC FIELD

Curriculum 2.0 Algebra 2: Unit 2-Topic 1, SLT 6 Name: Operations
Curriculum 2.0 Algebra 2: Unit 2-Topic 1, SLT 6 Name: Operations

... their sum is 0. This eliminates the imaginary part of the complex number, leaving only the sum of the real parts. The sum of the real parts will always be double the real part in the original complex numbers. Multiplying: Using the distributive property, multiplying complex conjugates will always re ...
Unit 3B Notes: Graphs of Polynomial Functions
Unit 3B Notes: Graphs of Polynomial Functions

The Multivariate Resultant is NP-hard in any Characteristic
The Multivariate Resultant is NP-hard in any Characteristic

Factoring Polynomials
Factoring Polynomials

Graphing absolute values on a numberline
Graphing absolute values on a numberline

Math_Practices_HS Sample_Problems
Math_Practices_HS Sample_Problems

Document
Document

Graphs of Polynomial Functions
Graphs of Polynomial Functions

A Quick Review of MTH070
A Quick Review of MTH070

TRANSCENDENTAL NUMBERS
TRANSCENDENTAL NUMBERS

Improvement of convergence condition of the square
Improvement of convergence condition of the square

of Bits of Algebraic and Some Transcendental Numbers
of Bits of Algebraic and Some Transcendental Numbers

Multiplying Polynomials
Multiplying Polynomials

Solving Equations in Rings
Solving Equations in Rings

Number Fields
Number Fields

< 1 ... 387 388 389 390 391 392 393 394 395 ... 480 >

Fundamental theorem of algebra

The fundamental theorem of algebra 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 an 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 roots. The equivalence of the two statements can be proven through the use of successive polynomial division.In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when the study of algebra was mainly concerned with the solutions of polynomial equations with real or complex coefficients.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report