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NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1 - Polynomials
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
- NCERT Solutions Class 10 Maths Chapter 2: Exercise 2.1 PDF
- Access Solution of Polynomials Class 10 Chapter 2 Exercise: 2.1
- Topics covered in Chapter 1 Number System: Exercise 1.1
- NCERT Solutions of Class 10 Subject Wise
- NCERT Exemplar Solutions of Class 10 Subject Wise
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.
Access Solution of Polynomials Class 10 Chapter 2 Exercise: 2.1
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).
Answer: The number of zeroes of p(x) is one, as the graph intersects the x-axis only once.
Answer: The number of zeroes of p(x) is three, as the graph intersects the x-axis thrice.
Answer: The number of zeroes of p(x) is two, as the graph intersects the x-axis twice.
Answer: The number of zeroes of p(x) is four, as the graph intersects the x-axis four times.
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.
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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: 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: What is meant by the zero of the polynomial?
A:
The value of x for which the polynomial becomes zero.
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 ?
Hello,
Yes, you can give the CBSE board exam in 2027.
If your date of birth is 25.05.2013, then in 2027 you will be around 14 years old, which is the right age for Class 10 as per CBSE rules. So, there is no problem.
Hope it helps !
Hello! If you selected “None” while creating your APAAR ID and forgot to mention CBSE as your institution, it may cause issues later when linking your academic records or applying for exams and scholarships that require school details. It’s important that your APAAR ID correctly reflects your institution to avoid verification problems. You should log in to the portal and update your profile to select CBSE as your school. If the system doesn’t allow editing, contact your school’s administration or the APAAR support team immediately so they can correct it for you.
Hello Aspirant,
Here's how you can find it:
-
School ID Card: Your registration number is often printed on your school ID card.
-
Admit Card (Hall Ticket): If you've received your board exam admit card, the registration number will be prominently displayed on it. This is the most reliable place to find it for board exams.
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School Records/Office: The easiest and most reliable way is to contact your school office or your class teacher. They have access to all your official records and can provide you with your registration number.
-
Previous Mark Sheets/Certificates: If you have any previous official documents from your school or board (like a Class 9 report card that might have a student ID or registration number that carries over), you can check those.
Your school is the best place to get this information.
Hello,
It appears you are asking if you can fill out a form after passing your 10th grade examination in the 2024-2025 academic session.
The answer depends on what form you are referring to. Some forms might be for courses or examinations where passing 10th grade is a prerequisite or an eligibility criteria, such as applying for further education or specific entrance exams. Other forms might be related to other purposes, like applying for a job, which may also have age and educational requirements.
For example, if you are looking to apply for JEE Main 2025 (a competitive exam in India), having passed class 12 or appearing for it in 2025 are mentioned as eligibility criteria.
Let me know if you need imformation about any exam eligibility criteria.
good wishes for your future!!
Hello Aspirant,
"Real papers" for CBSE board exams are the previous year's question papers . You can find these, along with sample papers and their marking schemes , on the official CBSE Academic website (cbseacademic.nic.in).
For notes , refer to NCERT textbooks as they are the primary source for CBSE exams. Many educational websites also provide chapter-wise revision notes and study material that align with the NCERT syllabus. Focus on practicing previous papers and understanding concepts thoroughly.
Popular CBSE Class 10th Questions
A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is
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An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
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A particle is projected at 600 to the horizontal with a kinetic energy . The kinetic energy at the highest point
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In the reaction,
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How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?
| Option 1)
0.02 |
Option 2)
3.125 × 10-2 |
| Option 3)
1.25 × 10-2 |
Option 4)
2.5 × 10-2 |
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