Polynomials
Revision Notes for Class 10
Introduction
A polynomial is an expression consisting of variables, coefficients, and exponents that are combined using addition, subtraction, and multiplication.
Example: [math] p(x) = 4x + 2 [/math] (degree 1), [math] p(x) = 5x^3 – 4x^2 + x – 2 [/math] (degree 3)
Types of Polynomials
- Linear Polynomial: Degree 1 (e.g., [math] 2x – 3 [/math])
- Quadratic Polynomial: Degree 2 (e.g., [math] ax^2 + bx + c [/math])
- Cubic Polynomial: Degree 3 (e.g., [math] ax^3 + bx^2 + cx + d [/math])
Key Formulae
1. Zeroes of a Polynomial
A real number [math] k [/math] is a zero of a polynomial [math] p(x) [/math] if [math] p(k) = 0 [/math].
2. Relationship between Zeroes and Coefficients
For [math] p(x) = ax^2 + bx + c [/math]:
Sum of zeroes = [math] -\frac{b}{a} [/math]
Product of zeroes = [math] \frac{c}{a} [/math]
Sum of zeroes = [math] -\frac{b}{a} [/math]
Product of zeroes = [math] \frac{c}{a} [/math]