Class 10 Maths - CBSE
Polynomials
The Class 10 CBSE chapter on Polynomials builds upon your previous knowledge by focusing heavily on quadratic polynomials and their graphical representations. You will learn about the geometrical meaning of the zeroes of a polynomial and the crucial relationship between zeroes and coefficients. The chapter also introduces the Division Algorithm for polynomials, which helps in finding all zeroes when some are given. This chapter is a fundamental building block for algebra and carries significant weight in board exams, testing both your conceptual understanding and algebraic manipulation skills.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree, which determines the maximum number of zeroes the polynomial can have.
Geometrical Meaning of Zeroes
The zeroes of a polynomial are precisely the x-coordinates of the points where the graph of the polynomial intersects the x-axis.
Relationship between Zeroes and Coefficients
For a quadratic polynomial ax squared plus bx plus c, the sum of zeroes is equal to minus b over a, and the product of zeroes is c over a.
Division Algorithm for Polynomials
It states that if p(x) and g(x) are two polynomials with g(x) not equal to zero, we can find polynomials q(x) and r(x) such that p(x) equals g(x) multiplied by q(x) plus r(x).
Important Formulas
Board Exam Info
In the CBSE Class 10 Mathematics board exam, this chapter typically carries around 3 to 5 marks. Common question types include finding the zeroes of a quadratic polynomial and verifying the relationship with coefficients, forming a quadratic polynomial given its sum and product of zeroes, and applying the division algorithm.
Frequently Asked Questions
What is the difference between a zero of a polynomial and a root of an equation?
A zero of a polynomial p(x) is the value of x where p(x) = 0, whereas a root refers to the value of x that satisfies an equation p(x) = 0. Conceptually they are often the same for a given expression, but zeroes apply to expressions and roots apply to equations.
How do I find a quadratic polynomial if only the sum and product of its zeroes are given?
You can directly use the standard formula: k * [x^2 - (Sum)x + (Product)], where k is any non-zero real number.
Can a quadratic polynomial have only one zero?
Yes, a quadratic polynomial can have one distinct zero (which actually means two equal real zeroes) if its graph touches the x-axis at exactly one point.
Learn Polynomials with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards