Polynomials Class 10 Maths Notes Chapter 2

Class 10 Maths Chapter 2 Polynomials Overview

"Polynomials" is the second chapter of class 10 maths.
In this chapter, we are going to study various types of polynomials such as linear polynomials, quadratic polynomials, and cubic polynomials.

This chapter is one of the most important chapters of maths because the types of polynomials, we are going to study in this chapter will become a chapter in the future such as for linear polynomials there is a chapter linear equations in 10th class.

In this chapter, polynomial, we are also going to study the relationship between the zeroes and coefficients for both quadratic and cubic polynomials.

Notes of NCERT Class 10 Maths Chapter 2

1. Algebraic Polynomials

Polynomials are classified based on the highest degree of the polynomial. The highest degree of the polynomial is the number of zeroes the polynomial have.

(i) Linear Polynomials = Highest degree is 1.
Standard form = ax + b (a and b are real numbers and a ≠ 0)
For ex = x + 1, x + 2, 2x + 4

(ii) Quadratic Polynomials = Highest degree is 2.
Standard form = ax² + bx + c (a, b and c are real numbers and a ≠ 0)
For ex = x² + 2x + 1, 2x² + 1, 5x² +3

(iii) Cubic Polynomials = Highest degree is 3.

Standard form = ax³ + bx² + cx + d (a, b, c and d are real numbers and a ≠ 0)

For ex = x³ + 2x² + x + 5, 6x³ + 3x² + d, 3x³ + 5x + 8

(iv) Bi-Quadratic Polynomials = Highest degree is 4.
General/Standard form = ax⁴ + bx³ + cx² + dx + e
For ex = 2x⁴ + 3x³ + 7x² + 5x + 4

2. Graphical Representation of Polynomials

The number of times the graph of the polynomial intersects the x is the number zeroes the polynomial have.

(i) Graph of Linear Polynomial = Always a straight line.

(ii) Graph of Quadratic Polynomials = Always curved to resemble 'U' shape also known as a parabola.

(iii) Graph of Cubic Polynomial = Always curved two times.

3. Relationship between the zeroes and coefficients

(i) For quadratic polynomials = If the equation is ax² + bx + c.
α + β = -b/a
αβ = c/a

(ii) For cubic polynomials = If the equation is ax³ + bx² + cx + d.
α + β + γ = -b/a
αβ + βγ + γα = c/a
αβγ = d/a

Conclusion 

Hey guys by learning the above notes on class 10 maths chapter 2 polynomials you will top the exams for sure.

You can check more notes for class 10 on our website to study because on our website "NCERTclass 10", we upload study material for class 10.

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