NCERT Solutions for class 10 Maths chapter 2 Polynomials all exercises in Hindi and English medium (UP Board and CBSE Board) PDF format. It is free to download updated for new academic session 2022-23 CBSE and UP Board high school students.

## Class 10 Maths chapter 2 all Exercises Solutions

### NCERT Solutions for class 10 Maths chapter 2

Students are now using NCERT Textbooks for their final exams. So, they can download UP Board Solutions for Class 10 Maths Chapter 2 from this page in PDF format. Assignments and Revision tests are given below in the format of PDF file.

• ### 10th Maths Chapter 2 Exercise 2.4

All the solutions are in Hindi as well as English Medium format. Videos related to each exercises are also given below with complete explanation and examples. Students Download Class 10 NCERT Solutions Apps 2022-2023 for offline use. Download here Bahupad ki prashnavali 2.1, 2.2, 2.2, 2.4. Solutions are available in Hindi and English. Visit to Discussion Forum to ask your doubts and share your knowledge with the other users. For any education help, you can contact us without any hesitation.

• ### Class 10 Maths Chapter 2 Practice Tests with Answers

 Class: 10 Maths (English and Hindi Medium) Chapter 2: Polynomials

### 10th Maths Chapter 2 Solutions

Class 10 Exercises solutions are solved in both English as well as Hindi medium in order to help all type of students following latest CBSE Syllabus 2022-23. In prashnavali 2.1, 2.2, 2.3 and 2.4 Ganit Solutions, if there is any inconvenient to understand, please inform us, we will short out at our level best.

#### Class 10 Maths Chapter 2 Exercise 2.1 and 2.2 Solutions in Hindi Video

Class 10 Maths Chapter 2 Exercise 2.1 Solution in Hindi
Class 10 Maths Chapter 2 Exercise 2.2 Solution in Hindi

#### Class 10 Maths Chapter 2 Exercise 2.3 and 2.4 Solutions in Hindi Video

Class 10 Maths Chapter 2 Exercise 2.3 Solution in Hindi
Class 10 Maths Chapter 2 Exercise 2.4 Solution in Hindi

#### Class 10 Maths Exercise 2.1 & 2.2 Solutions in Video

Class 10 Maths Exercise 2.1 Solutions in Video
Class 10 Maths Exercise 2.2 Solutions in Video

#### Class 10 Maths Exercise 2.3 & 2.4 Solutions in Video

Class 10 Maths Exercise 2.3 Solutions in Video
Class 10 Maths Exercise 2.4 Solutions in Video

#### Zeros of Polynomials

The value(s) of the variable for which the value of a polynomial in one variable is zero is (are) called zero(s) of the polynomial. To verify the relationship between the zeroes and coefficients of a given quadratic polynomial, we can find the zeroes of p(x) by factorisation. By taking sum and product of these zeros, we can verify the following results. 1. An elegant way of dividing a polynomial by a liner polynomial was introduced by Paolo Ruffin in 1809. His method is known as Synthetic division, which facilitates the division of a polynomial by a linear polynomial or binomial of the form x – a with the help of the coefficients involved.
2. Determining the zeros of polynomials, or finding roots of algebraic equations is among the oldest problems in mathematics. The modern way, we use today only developed beginning in the 15th century. Before that, linear equations were written out in words.
###### What is the History of the mathematical notations?

1. The use of the equal to (=) sign is in Robert Recorde’s book (The Whetstone of Witte in 1557). Plus sign (+) the sign of addition, minus sign (−) the sign of subtraction and the use of an alphabet for an unknown variable in Michael Stifel’s book (Arithemetica integra in 1544).
2. René Descartes, in 1637, introduced the concept of plotting the graph of a polynomial equation. Just because of him, the popularity of use of letters of the alphabet to denote constants and letters from the end of the alphabet (x, y, z, etc.) to denote variables (like 2x, 3y, 7z, etc.) in the general formula for a polynomial in one variable.

### What do you understand by a Polynomial as per Class 10 Maths Chapter 2?

An algebraic expression, in which variable(s) does (do) not occur in the denominator, exponents of variable(s) are whole numbers and numerical coefficients of various terms are real numbers, is called a polynomial.

In other words,

1. No term of a polynomial has a variable in the denominator;
2. In each term of a polynomial, the exponents of the variable(s) are non-negative integers and
3. Numerical coefficient of each term is a real number.

The terms of a polynomial, having the same variable(s) and the same exponents of the variable(s), are called like terms. A polynomial of degree 2 is called a quadratic polynomial. The degree of a non-zero constant polynomial is taken as zero. When all the coefficients of variable(s) in the terms of a polynomial are zeros, the polynomial is called a zero polynomial. The degree of a zero polynomial is not defined.

### Do you know what is a monomial?

An algebraic expression or a polynomial, consisting of only one term, is called a monomial.

### Which type of polynomial is called a binomial?

An algebraic expression or a polynomial, consisting of only two terms, is called a binomial.

### Which type of algebraic expression is known as trinomial?

An algebraic expression or a polynomial, consisting of only three terms, is called a trinomial.

### How to make good Practice in Class 10 Maths Chapter 2 Polynomials?

Polynomials are said to be one of the important sections of mathematics, especially for Algebra. They’re used in most of the equations and topics of numerical operation in standard 10 and higher also. It wouldn’t be wrong, if we say polynomials are Building Blocks of Maths expressions. Here we will learn about how to solve all exercises of 10th Maths chapter 2. Before learning about the polynomial equation, we have to know its significant importance that makes the topic more interesting. Many Maths process that are done in everyday life can be interpreted as polynomials. With the help of polynomial equations, one can calculate the grocery bill for small and even distance travelled by light in space.

#### Step 1: State with basic knowledge of Polynomial to learn Exercise 2.1. We understand the significant importance of learning equations. Not just for sake of scoring good marks in class 10th Board exams for better understanding also. Few equation had been first solved in 1540 by Ludovico Ferrari. Most of his work is not included in the syllabus of 10th Maths Chapter 2. Exercise 2.1 is based on zeroes of a polynomials. Here we will learn to find the zeroes of Polynomials using the intersections on x-axis. In class 10th NCERT books expect you to master the strategy to recognize with the input of formulae and solve it. This strategy must be learnt to obtain the answer to the polynomial equation. In terms of the solution of the cubic equations or the other methods you follow.

#### Step 2: Focus on the relationship between zeros and coefficient of variables. In class 10th Maths Exercise 2.2, we have to relate the coefficient of variable with the zeros. In this exercise or such cases keep them interested to find new ways to solve it while keeping the interest alive is a daunting task. This is why our NCERT Solutions for class Maths 10 contain various representations. These solutions to students addressing their different learning styles. Different videos and PDFs representations include using manipulative, showing tips, videos, presenting the problems, solving and showing symbolic offerings. For instance, in ideal classrooms, teachers show various ways to solve the same problem, whether cubic, quadratic equations, or some other. Students are being encouraged to solve them with their creative styles. It is only when there are exposed to all the various methods before.

#### Step 3: Use the contradiction method to prove an irrational number as irrational. Here, in 10th Maths Exercise 2.3, we learn the ways to prove a number as irrational if it is. Most High school students are struggling to prepare to face the most important exam as this decides their future studies. While preparing the NCERT solution for Class 10th Maths third exercise, must learn about the facts related to an irrational numbers. A lot of students memorized the polynomial, quadratic formula in middle school. But have you ever tried the cubic formula? It is quite complicated and not nearly as easy to derive if you are now aware about the relational between roots and coefficient. But if get to learn with us you will delve deeper into solving equations. This will make you confident in questions related to 10th Maths Exercise 2.3.

#### Step 4: Identify the terminating and non-terminating numbers. If we learn the concepts systematically, it quite easy to understand about terminating or non-terminating rational numbers. If this is possible we would always be able to demonstrate the application of all the equations in daily life as a polynomial. In the real world, that can be eye-opening for the students if they relate the Maths work with day to day activities. When concepts cannot be demonstrated in that manner, we can still show how it is can work in Maths. This is possible only when you are interested to know about the development of the method over time. This is why the NCERT Maths class 10th chapter contains fragments of famous mathematicians’ history. Watching videos of such terms might take a few minutes but are effective practices.

#### Step 5: Revise the chapter to build Structural Approach towards Learning. We are here at Tiwari Academy to understand the value of time for scholars, who is about doing extra efforts to delve deep into studies. Keep the objective of learning clear. That can help you in a quick formative assessment to determine the knowledge you gain. You will know where the lesson will go next time. Always revise the chapter in a sufficient interval of time. We understand the importance of focus during the preparation. This is why you should get our PDF and video and work offline. Some students like more physical work than reading to understand concepts but the polynomial equations are all about the writing practice until perfection. We suggest you practice the 10th NCERT Maths MCQs, exemplar, and practice papers so that you can reinforce the knowledge.

### What are real life applications of class 10th mathematics chapter 2?

Some real life applications of class 10th mathematics chapter 2 (Polynomials) are:

1. Polynomials can be used to model different types of situations, like in the stock market to see how prices will vary with time.
2. In physics also polynomials are used to describe the trajectory of projectiles.
3. Polynomials used in industries and construction field also.
Polynomials are useful for every person and in every field.

### How many exercises, questions and examples are there in chapter 2 of 10th Maths?

There are in all 4 exercises in class 10 mathematics chapter 2 (Polynomials).
In first exercise (Ex 2.1), there is only 1 question having 6 parts.
In second exercise (Ex 2.2), there are 2 questions and each question have 6 parts.
In third exercise (Ex 2.3), there are 5 questions.
In fourth exercise (Ex 2.4 optional exercise), there are 5 questions.
So, there are total 13 questions in class 10 mathematics chapter 2 (Polynomials).
In this chapter there are in all 9 examples. Example 1 is based on Ex 2.1, Examples 2, 3, 4, 5 are based on Ex 2.2 and Examples 6, 7, 8, 9 are based on Ex 2.3.

### Which questions and examples are important in Class 10 Maths Chapter 2?

In first exercise (Ex 2.1) there is only 1 question with 6 parts and all the part of this question are equally important. In second exercise (Ex 2.2) all questions are important.
In third exercise (Ex 2.3) Q3, 4, 5 are important and last but not the least, in fourth exercise (Ex 2.4 Optional exercise) Q2, 3, 4, 5 are important.
Important examples of chapter 2 (Polynomials) class 10th mathematics are example 1, 2, 3, 4, 8, 9.

### What should we recall before starting chapter 2 of 10th Maths?

Before starting class 10th mathematics chapter 2 (Polynomials), students should recall chapter 2 (Polynomials) of class 9th mathematics.                           