---
title: "NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1"
url: https://www.swavid.com/maths/class/10/chapter/polynomials/ncert-solutions/exercise-2-1
dateModified: 2026-10-07T15:48:01+00:00
---

# NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1

Chapter 2: Polynomials. Every question from Exercise 2.1, with full working and the final answer.

Free PDF (5 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-10/swavid-ncert-solutions-class-10-maths-chapter-2-polynomials-68994c428f.pdf

## EXERCISE 2.1

### Question 1

*6 marks · Short answer*

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.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi)

**Part (i)**

1. The graph of $y = p(x)$ intersects the $x$-axis at exactly one point.
2. Therefore, the number of zeroes is 1.

Answer (i): 1

**Part (ii)**

1. The graph of $y = p(x)$ intersects the $x$-axis at exactly one point.
2. Therefore, the number of zeroes is 1.

Answer (ii): 1

**Part (iii)**

1. The graph of $y = p(x)$ intersects the $x$-axis at three distinct points.
2. Therefore, the number of zeroes is 3.

Answer (iii): 3

**Part (iv)**

1. The graph of $y = p(x)$ intersects the $x$-axis at two distinct points.
2. Therefore, the number of zeroes is 2.

Answer (iv): 2

**Part (v)**

1. The graph of $y = p(x)$ intersects the $x$-axis at four points.
2. Therefore, the number of zeroes is 4.

Answer (v): 4

**Part (vi)**

1. The graph of $y = p(x)$ intersects or touches the $x$-axis at three points.
2. Therefore, the number of zeroes is 3.

Answer (vi): 3

**Answer:** The number of zeroes in cases (i) to (vi) are 1, 1, 3, 2, 4, and 3 respectively.

> Common mistake: Counting the number of times the graph intersects the y-axis or counting local maxima and minima instead of intersection points with the x-axis.

## Related pages

- [All Chapter 2 NCERT solutions](https://www.swavid.com/maths/class/10/chapter/polynomials/ncert-solutions)
- [Exercise 2.2](https://www.swavid.com/maths/class/10/chapter/polynomials/ncert-solutions/exercise-2-2)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student