Class 10 Maths - HARYANA
Polynomials
The chapter Polynomials in Class 10 Mathematics builds upon your previous knowledge of algebraic expressions, focusing primarily on linear and quadratic polynomials. You will learn about the geometrical meaning of the zeroes of a polynomial and the relationship between zeroes and coefficients of a quadratic polynomial. Additionally, the division algorithm for polynomials will help you understand higher-degree equations. This chapter is a fundamental stepping stone in algebra and carries significant weight in the Haryana Board (BSEH) examinations, frequently appearing in both objective and short-answer sections.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree. For example, the degree of 3x² + 5x - 2 is 2.
Geometrical Meaning of Zeroes
The zeroes of a polynomial p(x) are the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
Relationship between Zeroes and Coefficients
For a quadratic polynomial ax² + bx + c, the sum of zeroes is -b/a and the product of zeroes is c/a.
Formation of Quadratic Polynomial
A quadratic polynomial can be directly formed using the formula when its sum of zeroes and product of zeroes are given.
Division Algorithm for Polynomials
It states that if p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x).
Important Formulas
Board Exam Info
In the Haryana Board (BSEH) Class 10 Mathematics examination, the Chapter on Polynomials typically carries around 4 to 6 marks. Common question types include finding the zeroes of a quadratic polynomial and verifying the relationship between zeroes and coefficients, forming a quadratic polynomial given its sum and product of zeroes, and simple division algorithm problems.
Frequently Asked Questions
What is the difference between a polynomial and an equation?
A polynomial is an algebraic expression consisting of variables and coefficients with non-negative integer exponents (e.g., 2x + 3), whereas an equation includes an equality sign setting two expressions equal to each other (e.g., 2x + 3 = 5).
How do I find the number of zeroes from a graph?
Count the total number of times the given curve or line intersects the x-axis. The number of intersection points equals the number of real zeroes.
Can a quadratic polynomial have only one zero?
Yes, a quadratic polynomial can have one real zero if its graph touches the x-axis at exactly one point, which means the two zeroes are equal in value.
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