Proofs of Descartes Rule & Polynomial Roots in College Algebra Texts

  • Context: Undergrad 
  • Thread starter Thread starter symbolipoint
  • Start date Start date
  • Tags Tags
    Polynomial Roots
Click For Summary
SUMMARY

The discussion centers on the lack of rigorous proofs for Descartes' Rule of Signs and the tests for upper and lower bounds of real zeros in College Algebra textbooks. Participants noted that while these concepts are frequently mentioned, they are rarely accompanied by formal proofs. A specific resource, a 7-page document titled "POLYTHEOREMS," was highlighted as the only found rigorous proof. Participants seek recommendations for textbooks or courses that include these proofs in their curriculum.

PREREQUISITES
  • Understanding of polynomial functions and their properties
  • Familiarity with Descartes' Rule of Signs
  • Knowledge of real number theory
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Research "POLYTHEOREMS" for a detailed proof of Descartes' Rule of Signs
  • Explore advanced College Algebra textbooks that include rigorous proofs
  • Investigate university courses that cover polynomial root theorems
  • Study mathematical proof techniques relevant to algebraic concepts
USEFUL FOR

Mathematics students, educators teaching College Algebra, and anyone interested in the theoretical foundations of polynomial functions and their properties.

symbolipoint
Homework Helper
Education Advisor
Gold Member
Messages
7,691
Reaction score
2,121
A few of the (assumed to be good) textbooks on College Algebra discuss the use of Descartes Rule of Signs, and a test for upper and lower bounds for real zeros for polynomial functions; but these ideas are never proved in the books that I found. In which college course, and in which Mathematics textbooks are proofs for these ideas found?
 
Mathematics news on Phys.org
Only rigorous proof i found, it goes for 7 pages.

http://homepage.smc.edu/kennedy_john/POLYTHEOREMS.PDF
 
Last edited by a moderator:

Similar threads

High School Upper and Lower Bounds of Polynomials
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Does Descartes Rule of Signs Count Multiplicities in Its Upper Bound for Roots?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Lower and Upper bounds of Polynomial equations
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Proof of a fact about real numbers - transcendental and algebraic
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Proof of x^3+a^2x+b^2=0 roots question
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What can be deduced about the roots of this polynomial?
  • · Replies 3 ·
Replies
3
Views
3K
Questions about proof of upper and lower bound theorem for polynomials
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Practice With Proofs? (Algebra, Trig, and Calc)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad On the topological proof of the Fundamental Theorem of Algebra
  • · Replies 18 ·
Replies
18
Views
4K
Proving convergence of rational sequence
  • · Replies 2 ·
Replies
2
Views
2K