The Fundamental Theorem of Algebra

Click For Summary

Discussion Overview

The discussion revolves around the Fundamental Theorem of Algebra, specifically focusing on the interpretation of a statement regarding polynomials and their linear factors over the complex numbers. Participants explore the meaning of a notation encountered in an old textbook, questioning its clarity and correctness.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the meaning of the notation "a^n ≠ 0" in the context of polynomials, suggesting it might refer to a complex index.
  • Another participant proposes that the notation is likely a misprint for "where a0 ≠ 0," indicating the polynomial is of genuine nth-degree.
  • Several participants engage in testing and confirming the functionality of their input, indicating a focus on practical application of the polynomial notation.

Areas of Agreement / Disagreement

There is no clear consensus on the interpretation of the notation, with one participant suggesting a misprint while another seeks clarification. The discussion remains somewhat unresolved regarding the original statement's intent.

Contextual Notes

The discussion highlights potential ambiguities in mathematical notation and the importance of context in interpreting such statements. There are unresolved assumptions regarding the textbook's content and notation.

SprucerMoose
Messages
62
Reaction score
0
Hi all,
I'm currently flicking through and old textbook and came across the following.

"Every polynomial of the form
P(z)%20=%20a_{0}x^{n}%20+%20a_{1}x^{n-1}%20+%20a_{2}x^{n-2}%20+%20...%20+%20a_{n-1}x%20+%20a_{n}.gif
, where
gif.latex?a^{n}\neq0.gif
has n linear factors over C...". What does it mean by [URL]http://latex.codecogs.com/gif.latex?a^{n}\neq0?[/URL] Is this referring to some kind of complex index? This is all that is written and nothing precedes it. I just don't quite understand the
gif.latex?a^{n}\neq0.gif
.Edit: Latex kind of fixed
 
Last edited by a moderator:
Mathematics news on Phys.org
Hi SprucerMoose! :smile:

(try using the X2 and X2 icons just above the Reply box :wink:)

it must be a misprint for "where a0 ≠ 0" …

in other words, where it's a genuine nth-degree polynomial :smile:
 
Ah, I see. Thank you very much.Testing...

a2 + a0 + a1

Edit: It works!
 
SprucerMoose said:
Testing...

a2 + a0 + a1

Edit: It works!

Now you really are sprucer! :biggrin:
 
SprucerMoose said:
Ah, I see. Thank you very much.


Testing...

a2 + a0 + a1

Edit: It works!
Do you mean a2 + a0 + a1?
 
Mark44 said:
Do you mean a2 + a0 + a1?

Do you mean a2 + a0 + a1?
 
Top that! :smile:

SprucerMoose wins! :biggrin:​
 

Similar threads

Undergrad Question about the Fundamental Theorem of Algebra
  • · Replies 14 ·
Replies
14
Views
3K
High School Extending the Fundamental Theorem of Arithmetic to the rationals
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad Why the Fundamental Theorem of Algebra & Calculus are Called "Fundamental
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad On the topological proof of the Fundamental Theorem of Algebra
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad Fundamental theorem of algebra and factoring?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Can Fundamental Theorem Algebra be proven by simple DOF?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Fundamental representation and adjoint representation
  • · Replies 27 ·
Replies
27
Views
4K
Graduate So-called Fundamental Theorem of Algebra
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Understanding the fundamental theorem of algebra
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Fundamental Theorem of Arithmetic - Bhattacharya et al
  • · Replies 5 ·
Replies
5
Views
4K