NCERT Solutions For Class 10 Maths Chapter 2 Polynomials

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.

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:

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.

Answers:

(i) No intersection with x-axis → 0 zeroes

(ii) Graph cuts x-axis 3 times → 3 zeroes

(iii) Graph cuts x-axis 3 times → 3 zeroes

(iv) Graph does not touch x-axis → 0 zeroes

(v) Graph cuts x-axis 4 times → 4 zeroes

(vi) Graph cuts x-axis 3 times → 3 zeroes

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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.