OLYMPIAD > POLYNOMIALS AND THEIR ZEROS
The interesting journey in finding roots.
Polynomials form a large part of algebra. A polynomial is simply an expression of constants and variables that are formed using the four basic operations. A zero or a root is the solution of one of the variables in the polynomial. While polynomials look boring by themselves, it is the relationship between polynomials and their zeros that creates some interesting theorems.
While the quadratic equation was solved since ancient times, one of the most famous story of the history of polynomials is solving the cubic equation and sequently more than degree 3. Finding such a solution was so treasured that the main suspects of Cardano and Tartaglic had a dispute of who found it first. After that century, the development of polynomials was coloured with interesting theorems like Galois theory.
Niccolo Fontana Tartaglia
Niels Henrik Abel
General Factor Theorem
Zeros-Coefficient Relationship
Fundamental Theorem of Algebra
Abstract Algebra
The interesting journey in finding roots.
While the quadratic equation was solved since ancient times, one of the most famous story of the history of polynomials is solving the cubic equation and sequently more than degree 3. Finding such a solution was so treasured that the main suspects of Cardano and Tartaglic had a dispute of who found it first. After that century, the development of polynomials was coloured with interesting theorems like Galois theory.
CONCEPT CONTENTS
> INTRODUCTION TO POLYNOMIALS
> QUADRATIC POLYNOMIALS
> LINEAR AND GENERAL FACTOR THEOREM
> ZERO-COEFFICIENT RELATIONSHIP
> DESCARTES'S RULE OF SIGNS
> FUNDAMENTAL THEOREM OF ALGEBRA
AMC QUESTIONS
> 1999 AHSME #17
> 2000 AMC10 #24
> 2003 AMC12B #9
> 2001 AMC12 #19
Notable Mathematicians
Gerolamo CardanoNiccolo Fontana Tartaglia
Niels Henrik Abel
Important Theorems
Linear Factor Theorem General Factor Theorem
Zeros-Coefficient Relationship
Fundamental Theorem of Algebra
Applications
GraphsAbstract Algebra
