CBSE Class 10 Maths Chapter 2: Polynomials NCERT Solutions

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NCERT Solutions PDF Class 10 PDF

This chapter focuses on understanding polynomials and their graphical representation. The NCERT Solutions for Class 10 Maths Chapter 2: Polynomials provide a detailed explanation of how to determine the number of zeroes of a polynomial by examining its graph. The solutions cover various graphical scenarios, illustrating the relationship between the x-intercepts of a graph and the zeroes of the corresponding polynomial. These solutions are designed to help students grasp the fundamental concepts of polynomials and their roots, aiding in exam preparation and building a strong foundation in algebra.

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Quick info

BoardCBSE
ClassClass 10
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 2: Polynomials

Chapter summary

Chapter 2: Polynomials for Class 10 Maths NCERT Solutions focuses on the graphical interpretation of zeroes. It explains how the number of times a polynomial's graph intersects the x-axis directly corresponds to the number of its real zeroes. The exercise provides several graphical examples for students to practice identifying these intersection points and determining the count of zeroes for different polynomial graphs.

Learning outcomes

  • Understand the definition of zeroes of a polynomial.
  • Interpret the graphical representation of polynomials.
  • Determine the number of zeroes of a polynomial from its graph.
  • Relate the x-intercepts of a graph to the zeroes of the polynomial.

Topics covered

Paper topics

  • Polynomials
  • Zeroes of a polynomial
  • Graphical representation of polynomials
  • Number of zeroes from a graph
  • X-intercepts
  • Relationship between zeroes and graph

Important topics

  • Finding the number of zeroes from a graph
  • Interpreting x-axis intersections
  • Graphical method for identifying zeroes

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Questions and Solutions

Question 1 (i)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 3 points

Solution: The number of zeroes of a polynomial p(x) is equal to the number of points where the graph of y = p(x) intersects the x-axis. In the given figure (i), the graph intersects the x-axis at three distinct points. Therefore, the polynomial p(x) has 3 zeroes.

Question 1 (ii)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 1 point

Solution: The number of zeroes of a polynomial p(x) corresponds to the number of points where its graph intersects the x-axis. In the given figure (ii), the graph intersects the x-axis at exactly one point. Hence, the polynomial p(x) has 1 zero.

Question 1 (iii)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 2 points

Solution: To find the number of zeroes of the polynomial p(x), we observe the number of times its graph, y = p(x), crosses or touches the x-axis. In figure (iii), the graph intersects the x-axis at two distinct points. Consequently, the polynomial p(x) has 2 zeroes.

Question 1 (iv)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 0 points

Solution: The number of zeroes of a polynomial p(x) is determined by the number of intersections of its graph y = p(x) with the x-axis. In the provided figure (iv), the graph does not intersect the x-axis at any point. Therefore, the polynomial p(x) has no real zeroes.

Question 1 (v)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 4 points

Solution: The number of zeroes of a polynomial p(x) is equivalent to the number of points where the graph of y = p(x) meets the x-axis. In figure (v), the graph intersects the x-axis at four distinct points. Thus, the polynomial p(x) has 4 zeroes.

Question 1 (vi)

The graph of y = p(x) is given in the following figure for some polynomial p(x). Find the number of zeroes of p(x).

Graph of y=p(x) intersecting x-axis at 3 points, touching at one point

Solution: The number of zeroes of a polynomial p(x) is found by counting the number of points where its graph y = p(x) intersects or touches the x-axis. In figure (vi), the graph intersects the x-axis at three points. Therefore, the polynomial p(x) has 3 zeroes.

Common mistakes

  • Confusing x-intercepts with y-intercepts.
  • Miscounting the number of intersections with the x-axis.
  • Assuming any intersection with the y-axis indicates a zero.

Revision tips

  • Focus on the definition: a zero is where the graph crosses the x-axis.
  • Practice identifying x-intercepts in various graph orientations.
  • Review each graph carefully to ensure all intersections are counted.
  • Understand that touching the x-axis counts as an intersection.

Practice MCQs

Q1. What does the number of zeroes of a polynomial p(x) represent graphically?

Q2. If a graph of y = p(x) does not intersect the x-axis at all, how many zeroes does the polynomial have?

Q3. A graph intersects the x-axis at exactly one point. What can be said about the zeroes of the polynomial?

Q4. For the graph of y = p(x), what does a point where the graph touches the x-axis signify?

Frequently asked questions

What is the main concept covered in these NCERT Solutions for Class 10 Maths Chapter 2?

These solutions focus on understanding the relationship between the graph of a polynomial and its zeroes. Specifically, they explain how to determine the number of zeroes by counting the points where the graph intersects the x-axis.

How do these solutions help in exam preparation?

By providing clear explanations and graphical examples, these solutions help students visualize and understand the concept of zeroes from a graphical perspective, which is a common topic in exams.

What does it mean if a polynomial's graph intersects the x-axis at multiple points?

If a polynomial's graph intersects the x-axis at multiple points, it means the polynomial has that many distinct real zeroes.

Does touching the x-axis count as an intersection for finding zeroes?

Yes, if the graph of a polynomial touches the x-axis at a point, it is considered an intersection, and that point represents a zero of the polynomial.

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