Class 9 Maths - UP
Linear Polynomials
In this chapter of Class 9 Mathematics for Uttar Pradesh (UPMSP) students, you will study linear polynomials, which are algebraic expressions of the form ax + b where a and b are real numbers and a is not equal to zero. The chapter builds a strong foundation in algebra by introducing you to the degree of a polynomial, finding the value of a polynomial for given values of variables, and calculating the zeroes of a linear polynomial. Understanding these fundamental concepts is crucial for solving linear equations and higher-level algebraic problems in board exams.
Start Learning FreeKey Concepts
Polynomial
An algebraic expression consisting of variables and coefficients, where the exponent of the variable is a whole number.
Degree of a Polynomial
The highest power of the variable in a polynomial expression. For a linear polynomial, the degree is always 1.
Linear Polynomial
A polynomial of degree 1, generally represented in the standard form p(x) = ax + b, where 'a' and 'b' are constants and a != 0.
Zero of a Polynomial
The real value of the variable 'x' for which the value of the polynomial becomes zero, written as p(x) = 0.
Value of a Polynomial
The numerical value obtained by substituting a specific numerical value for the variable in the given polynomial.
Important Formulas
Board Exam Info
In the Uttar Pradesh (UPMSP) Class 9 Mathematics examination, this chapter along with polynomials generally carries around 4 to 6 marks. Common question types include finding the value of a polynomial at a given point, verifying whether a given number is a zero of the polynomial, and finding the zero of a linear polynomial.
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 and sets the polynomial to zero (like 2x + 3 = 0).
Can 'a' be zero in a linear polynomial ax + b?
No, 'a' cannot be zero because if a = 0, the term 'ax' becomes zero, leaving only the constant 'b', which is a constant polynomial of degree zero, not a linear polynomial.
How do I find the zero of a linear polynomial?
To find the zero of a polynomial p(x) = ax + b, set the polynomial equal to zero (ax + b = 0) and solve for x, which gives x = -b/a.
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