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

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

Updated on Apr 29, 2025 04:48 PM IST | #CBSE Class 10th

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

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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.

1635918537229

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

1635918562539

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

1635918572380

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

1635918582058

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

1635918606641

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


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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.

JEE Main Important Mathematics Formulas

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

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)

1. What is the graph representation of polynomials according to NCERT syllabusClass 10 Maths?

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.

2. What is meant by the zero of the polynomial?

The value of x for which the polynomial becomes zero. 

3. How are the graphs plotted?

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).

4. Which graph represents the polynomial with infinite zeros?

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

5. Which graph represents the polynomial with no solution?

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

6. Is the degree of the polynomial always equal to the number of zeroes?

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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Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?

Hello

Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.

1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.

2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.

3. Counseling and Seat Allocation:

After the KCET exam, you will need to participate in online counseling.

You need to select your preferred colleges and courses.

Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.

4. Required Documents :

Domicile Certificate (proof that you are a resident of Karnataka).

Income Certificate (for minority category benefits).

Marksheets (11th and 12th from the Karnataka State Board).

KCET Admit Card and Scorecard.

This process will allow you to secure a seat based on your KCET performance and your category .

check link for more details

https://medicine.careers360.com/neet-college-predictor

Hope this helps you .

Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

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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

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

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

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} 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

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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