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

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

    #CBSE Class 10th
    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.

    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.

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    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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