Class 9 Maths - MP
Linear Polynomials
In this chapter, Madhya Pradesh Board (MPBSE) Class 9 students will explore linear polynomials, which are algebraic expressions of the form ax + b where 'a' is non-zero. You will learn how to find the degree of a polynomial, evaluate polynomials for given values of variables, and find their zeroes. Understanding zeroes of a polynomial is crucial because it connects algebraic equations to graphical representations. This chapter forms the foundation for solving linear equations in two variables and quadratic equations in higher classes. Scoring well in this chapter is essential as it frequently features in MPBSE board exam short-answer questions.
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 highest power of the variable is always 1.
Linear Polynomial
A polynomial of degree 1 is known as a linear polynomial. Its general standard form is written as ax + b, where 'a' and 'b' are real numbers and a ≠ 0.
Value of a Polynomial
The value obtained by substituting a specific numerical value for the variable in a polynomial p(x) is called the value of the polynomial at that point.
Zero of a Polynomial
A real number 'k' is called a zero of a polynomial p(x) if p(k) = 0. Geometrically, it represents the x-coordinate where the graph of the polynomial intersects the x-axis.
Finding the Zero of a Linear Polynomial
To find the zero of a linear polynomial p(x) = ax + b, set the polynomial equal to zero (ax + b = 0) and solve for x, which gives x = -b/a.
Important Formulas
Board Exam Info
In the Madhya Pradesh (MPBSE) Class 9 Mathematics examination, this chapter typically carries around 4 to 6 marks. Common question types include finding the value of a polynomial for a given number, checking whether a given value is a zero of the polynomial, and finding 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 like 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, '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 rather than a linear polynomial.
How do I find the zero of the linear polynomial p(x) = 2x + 4?
To find the zero, put p(x) = 0. So, 2x + 4 = 0, which means 2x = -4, giving x = -2. Thus, -2 is the zero of the polynomial.
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