Polynomials

Board: GSEB Class: 10

Chapter Overview

A polynomial p(x) in one variable x is an algebraic expression of the form a_n xⁿ + a_(n-1) x^n-1 + ... + a_1 x + a_0, where a_n != 0. The degree is the highest power. A zero of p(x) is a value k such that p(k) = 0. For a quadratic polynomial ax² + bx + c, sum of zeros = -b/a and product of zeros = c/a. The division algorithm states: p(x) = g(x) x q(x) + r(x), where degree of r(x) < degree of g(x). Graphical representation: zeros are x-intercepts of the graph.

Topics Covered

Polynomial Definition
Degree of Polynomial
Zeros of Polynomial
Relationship: Zeros and Coefficients
Quadratic Polynomials
Cubic Polynomials
Division Algorithm
Graphical Representation

Key Formulas

Zero of polynomial: p(k) = 0

Sum of zeros = -b/a (quadratic)

Product of zeros = c/a (quadratic)

Sum of zeros = -d/a (cubic)

Real-World Applications

Applications: Modeling real-world phenomena, curve fitting, physics (projectile motion).

Study Tips

Tip: Practice finding zeros by factorization

Tip: Memorize the relation between zeros and coefficients

Tip: Draw graphs to visualize zeros