Class 9 Maths - BIHAR
Linear Polynomials
In the chapter 'Linear Polynomials' of Class 9 Mathematics under the Bihar School Examination Board (BSEB), students explore algebraic expressions where the highest power of the variable is one. This chapter builds a strong foundation for coordinate geometry and linear equations. Students learn to identify polynomial degrees, evaluate polynomials for given values, and find their zeros. Mastering this chapter is crucial because it forms the baseline for solving advanced algebraic problems, graphing linear equations, and scoring high marks in the BSEB Class 9 annual examinations and subsequent board exams.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree. For a linear polynomial, the degree is always equal to 1.
Linear Polynomial
A polynomial of degree one is called a linear polynomial, which can be expressed in the general form ax + b, where a and b are real numbers and a is not equal to 0.
Value of a Polynomial
The value obtained by substituting a specific numerical value for the variable in a given polynomial expression.
Zero of a Linear Polynomial
The real number k for which the value of the linear polynomial p(k) becomes zero is called the zero of the polynomial.
Geometric Meaning of Zero
The zero of a linear polynomial ax + b is the x-coordinate of the point where the graph of the equation y = ax + b intersects the x-axis.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 9 Mathematics exams, this chapter typically carries around 4 to 6 marks. Common question types include finding the degree of given polynomials, evaluating the value of a polynomial at a specific point, and calculating the zero of a given linear polynomial.
Frequently Asked Questions
What is the difference between a linear equation and a linear polynomial?
A linear polynomial is an algebraic expression of the form ax + b, whereas a linear equation includes an equality sign, such as ax + b = 0.
Can the coefficient 'a' be zero in a linear polynomial ax + b?
No, if a = 0, the term with the variable vanishes, reducing the expression to a constant number, which is not a linear polynomial.
How do we find the zero of a linear polynomial?
To find the zero of a linear polynomial p(x), set the polynomial equal to zero (p(x) = 0) and solve the resulting equation for x.
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