Class 9 Maths - WEST-BENGAL
Linear Polynomials
In this chapter of Class 9 Mathematics under the West Bengal Board (WBBSE), students explore Linear Polynomials, which are algebraic expressions where the highest power of the variable is one. You will learn about the standard form of a linear polynomial, how to find its value for given inputs, and how to determine its zero, which is the value of the variable that makes the polynomial equal to zero. This chapter forms the foundational building block for solving linear equations in one and two variables, playing a crucial role in scoring well in your board exams.
Start Learning FreeKey Concepts
Definition of Polynomial
An algebraic expression consisting of variables and coefficients, where the exponents of the variables are non-negative integers.
Degree of a Polynomial
The highest power of the variable present in the polynomial expression. For a linear polynomial, the degree is strictly 1.
Standard Form of a Linear Polynomial
Expressed algebraically as P(x) = ax + b, where 'a' and 'b' are real numbers and 'a' does not equal zero.
Zero of a Polynomial
The specific value of the variable for which the value of the polynomial becomes zero, found by solving the equation P(x) = 0.
Important Formulas
Board Exam Info
In the WBBSE Class 9 Mathematics examinations, this chapter typically carries around 3 to 5 marks. Common question types include finding the zero of a given linear polynomial, checking whether a specific value is a zero of the polynomial, and solving short-answer numerical problems based on the relation ax + b = 0.
Frequently Asked Questions
What is the difference between a linear equation and a linear polynomial?
A linear polynomial is an expression like ax + b, whereas a linear equation sets that expression equal to zero, written as ax + b = 0.
Why is the condition 'a ≠ 0' mandatory in a linear polynomial ax + b?
If 'a' becomes zero, the term with the variable disappears, leaving only the constant 'b', which reduces it to a constant polynomial of degree zero, not a linear polynomial.
How do I find the zero of the linear polynomial 3x - 6?
Set the polynomial equal to zero (3x - 6 = 0), solve for x to get 3x = 6, which gives x = 2. Thus, 2 is the zero of the polynomial.
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