NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1 - Polynomials

NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1 - Polynomials

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CBSE Class 10th Exam Date:01 Jan' 26 - 14 Feb' 26

Ramraj SainiUpdated on 30 May 2025, 02:21 PM IST

Polynomials enable the mathematical expression of repeating patterns through variable and coefficient components. The visual representation of polynomials shows us their behavioural patterns. The vital point to recognise consists of identifying when the graph crosses the x-axis. Mathematical functions gain greater depth through understanding, which becomes possible because of these significant values known as zeroes. A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

This Story also Contains

  1. NCERT Solutions Class 10 Maths Chapter 2: Exercise 2.1 PDF
  2. Access Solution of Polynomials Class 10 Chapter 2 Exercise: 2.1
  3. Topics covered in Chapter 1 Number System: Exercise 1.1
  4. NCERT Solutions of Class 10 Subject Wise
  5. NCERT Exemplar Solutions of Class 10 Subject Wise
NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1 - Polynomials
NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1 - Polynomials

Students can use the math NCERT Solutions for Class 10 based on the 2025–26 textbooks to better understand polynomial zeroes. Observing graphs within this exercise enables a clear identification of real zeroes based on graphical inspection. The solutions create a basic understanding, which helps students excel in algebraic learning while promoting real-world applications. The exercise functions as an essential tool for solidifying number type knowledge described in the NCERT Books, which leads to a complete understanding.

NCERT Solutions Class 10 Maths Chapter 2: Exercise 2.1 PDF

Access Solution of Polynomials Class 10 Chapter 2 Exercise: 2.1

Q1 (1) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the numbers of zeroes of p(x), in each case.

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Answer: The number of zeroes of p(x) is zero because the curve does not intersect the x-axis (it is parallel to the x-axis).

Q1 (2) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case

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Answer: The number of zeroes of p(x) is one, as the graph intersects the x-axis only once.

Q1 (3) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case

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Answer: The number of zeroes of p(x) is three, as the graph intersects the x-axis thrice.

Q1 (4) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case

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Answer: The number of zeroes of p(x) is two, as the graph intersects the x-axis twice.

Q1 (5) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case

1635918596067

Answer: The number of zeroes of p(x) is four, as the graph intersects the x-axis four times.

Q1 (6) The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case

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Answer: The number of zeroes of p(x) is three, as the graph intersects the x-axis thrice.


Also Read-

Topics covered in Chapter 1 Number System: Exercise 1.1

1. Graphical Representation of Polynomials: We examine how polynomials appear in graphical form alongside their relation to the degree level, which determines graphical shape.

2. Zeros of a Polynomial: Zeros of a Polynomial mean those points on the x-axis where the graph crosses the x-axis.

3. Analysing Graphs: The analysis of polynomial function graphs enables individuals to determine the number of real zeroes through interpretation.

4. Degree and Zeroes Relationship: Polynomial Degree Determines Maximum Zero Count by Establishing a Fundamental Relationship between these Two Elements.

Check Out-

NCERT Solutions of Class 10 Subject Wise

Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.

NCERT Exemplar Solutions of Class 10 Subject Wise

Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

Q: What is the graph representation of polynomials according to NCERT syllabusClass 10 Maths?
A:

Graph representation of a polynomial is plotting the values of x against the evaluated values of y and then analyzing the characteristics of the graphs whether it has no solution, one solution, two solutions or infinite solution etc depending upon how many times the graph intersects the x-axis.

Q: What is meant by the zero of the polynomial?
A:

The value of x for which the polynomial becomes zero. 

Q: How are the graphs plotted?
A:

Consider y=P(x) be any polynomial equation. To plot in the graph evaluate the value of y for each value of x and find ordered pair such as (considered value of x , evaluated value of y) plot it in the graph against the cartesian plane(a cartesian plane is a plane consisting of x-axis and y-axis).

Q: Which graph represents the polynomial with infinite zeros?
A:

 The graph in which there is a straight line coincident with the x-axis, it represents the graph with infinite solutions.

Q: Which graph represents the polynomial with no solution?
A:

Any graph which does not intersect the x-axis represents the graph with no solution.

Q: Is the degree of the polynomial always equal to the number of zeroes?
A:

No, it is not necessary.

For eg: A quadratic graph that does not intersect the x-axis has degree 2 but has 0 zeroes.

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Have a question related to CBSE Class 10th ?

Hi! If you’re looking for the Class 11 English half yearly question paper for 2025-26 (CBSE board), you’ll find the right resource once you check the link provided from Careers360. Solving previous or sample papers is a smart way to prepare, as it helps you understand the question types, marking scheme, and important topics. This practice will boost your confidence and help you manage your time well in the actual exam.
https://school.careers360.com/boards/cbse/cbse-class-11-half-yearly-sample-papers-2025-26

Hi dear candidate,

Could you please specify us the board of education for which you need the half yearly question papers of class X so that we can help you further.

Below are few links which may help you and it has all the subjects with English as well:

CBSE Class 10 Half Yearly Exam Question Paper 2025-26 with Answer Key & Analysis

ICSE Class 10 Half Yearly Sample Papers 2025-26 PDF (All Subjects)

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Hi dear candidate,

Can you please specify the board of education or state for which you need to know the exam pattern and syllabus so that we can guide you accordingly.

Since, most of the boards uses NCERT as base syllabus, you can refer to the link below:

NCERT Syllabus for Class 10 – All Subjects PDF Download 2025-26

Exam pattern:

CBSE 10th New Exam Pattern 2026- Marking Scheme, Subject-Wise Exam Pattern

BEST REGARDS

The CBSE Class 10th Board Exams for the 2026 session will follow the revised curriculum, emphasizing competency-based questions.

  • Conducting Body: Central Board of Secondary Education (CBSE).

  • Exam Period: The main theory exams are typically held between February and April 2026.

  • Grading: Based on marks in five main subjects plus internal assessment marks (often 20 marks per subject) provided by the school.

  • Passing Criteria: You must achieve at least 33% overall in each subject (theory + practical/internal assessment combined) to be declared pass.

Key Preparation Strategy

The most crucial element of your preparation is understanding the exam structure:

  • Syllabus: Strictly adhere to the rationalized syllabus released by CBSE for the 2025-26 academic year.

  • Practice: Your primary resource should be the latest sample papers and previous year question papers. These accurately reflect the format and types of competency questions being asked.

For the most comprehensive and official announcements, including the detailed time table and access to crucial practice materials, always check the official board updates, as tracked by Careers360: https://school.careers360.com/exams/cbse-class-10th .

HELLO,

If you want admission to 9th grade under the CBSE board in Andhra Pradesh , visit nearby CBSE affiliated schools during the admission period that is generally from January  to April or you can check the official websites of the schools in which you are interested for admission if they are accepting the admissions now .

After deciding the school and getting information about admission deadline from the school you can fill out the admission form with documents submission like your previous report card , transfer certificate and birth certificate , they make take entrance test or interview to confirm your admission

To know more visit :- https://school.careers360.com/schools/cbse-schools-in-andhra-pradesh

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