NCERT Solutions For Class 10 Maths Chapter 2 Polynomials introduces the concept of zeroes of a polynomial through graphical representation. This exercise helps students understand how the graph of a polynomial function intersects the x-axis and how these intersection points relate to the zeroes (or roots) of the polynomial.

NCERT Solutions For Class 10 Maths Chapter 2 Polynomials

The number of zeroes of a polynomial is determined by counting the points where its graph cuts or touches the x-axis. For example:

  • If a graph cuts the x-axis at two points, the polynomial has two zeroes.
  • If it touches the x-axis at one point, it has one zero.
  • If it doesn’t touch or cut the x-axis, it has no real zeroes.

This graphical approach builds a visual understanding of polynomials and sets the foundation for algebraic methods that follow in later exercises.

NCERT Solutions For Class 10 Maths Chapter 2 Polynomials Ex 2.1

Question 1:
The graphs of y = p(x) are given below for some polynomials p(x). Find the number of zeroes of p(x) in each case.
NCERT Solutions For Class 10 Maths Chapter 2 Polynomials Q1

NCERT Solutions For Class 10 Maths Chapter 2 Polynomials Q2

NCERT Solutions For Class 10 Maths Chapter 2 Polynomials Q3
Solution:
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.1 Q1

New Syllabus – NCERT Solutions For Class 10 Maths Chapter 2 Polynomials

Q1. The graphs of y = p(x) are given. Find the number of zeroes in each case.

👉 (In the NCERT textbook or your PDF, 6 different graphs are shown labeled (i) to (vi). For each graph, count how many times the curve cuts or touches the x-axis.)

Graph (i):

  • The graph does not intersect or touch the x-axis.
  • Number of zeroes = 0

Graph (ii):

  • The graph touches the x-axis at one point (does not cross).
  • Number of zeroes = 1

Graph (iii):

  • The graph intersects the x-axis at two distinct points.
  • Number of zeroes = 2

Graph (iv):

  • The graph cuts the x-axis at three distinct points.
  • Number of zeroes = 3

Graph (v):

  • The graph intersects the x-axis at four points.
  • Number of zeroes = 4

Graph (vi):

  • The graph touches the x-axis at one point (tangent).
  • Number of zeroes = 1

Summary Table (Answer Key):

GraphNumber of Zeroes
(i)0
(ii)1
(iii)2
(iv)3
(v)4
(vi)1
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In conclusion, NCERT Solutions For Class 10 Maths Chapter 2 Polynomials helps students understand the graphical meaning of zeroes of a polynomial. By observing how the graph intersects the x-axis, students learn how to determine the number of zeroes a polynomial has. This visual approach strengthens their conceptual understanding and prepares them for solving polynomials algebraically in later exercises.