Class 9 Maths - ODISHA
Linear Polynomials
The chapter 'Linear Polynomials' in Class 9 Mathematics under the Board of Secondary Education (BSE) Odisha introduces students to algebraic expressions involving variables and constants. You will learn about the degree of polynomials, identifying linear polynomials where the highest power of the variable is one, and finding their zeros. This chapter builds a strong foundation for solving linear equations in two variables and coordinate geometry in later classes. Mastering this topic is essential for scoring well in your BSE Odisha half-yearly and annual board examinations, as questions ranging from basic definitions to finding roots frequently appear.
Start Learning FreeKey Concepts
Polynomial in One Variable
An algebraic expression of the form p(x) = anx^n + ... + a1x + a0 where the exponents of x are non-negative integers and coefficients are real numbers.
Degree of a Polynomial
The highest power of the variable in a polynomial expression. For a linear polynomial, the degree is always equal to 1.
Linear Polynomial
A polynomial of degree 1, generally expressed in the standard form ax + b, where 'a' and 'b' are real numbers and a ≠ 0.
Zero of a Polynomial
A real value of the variable 'x' for which the value of the polynomial becomes zero, denoted as p(x) = 0.
Value of a Polynomial
The numerical value obtained by substituting a specific numerical value for the variable x in a given polynomial p(x).
Important Formulas
Board Exam Info
In the BSE Odisha Class 9 Mathematics examinations, polynomial chapters generally carry around 6 to 8 marks. Common question types include 1-mark objective questions (MCQs and fill-in-the-blanks) testing the degree or value of polynomials, 2-mark short answer questions on finding the zero of a linear polynomial, and 3-mark analytical problems.
Frequently Asked Questions
What is the difference between a linear equation and a linear polynomial?
A linear polynomial is an algebraic expression like 2x + 3, whereas a linear equation includes an equality sign, such as 2x + 3 = 0.
Can the coefficient 'a' be zero in a linear polynomial ax + b?
No, 'a' cannot be zero because if a = 0, the term with the variable disappears, leaving only a constant, which reduces it to a constant polynomial of degree zero.
How do I find the zero of the linear polynomial 3x - 6?
To find the zero, equate the polynomial to zero: 3x - 6 = 0. Solving for x gives 3x = 6, so x = 2.
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