NCERT Class 10 Maths – Chapter 2: Polynomials
Exercise 2.1 – Number of Zeroes of a Polynomial (Graphical Method)
Class: 10
Subject: Mathematics
Chapter: Polynomials
Exercise: 2.1
Concept Used:
The zeroes of a polynomial are the points where the graph of y = p(x) intersects the x-axis.
👉 Number of zeroes = Number of points where the graph cuts or touches the x-axis.
Question 1: Find the number of zeroes of p(x) in each case.
(i)
The graph is a straight horizontal line parallel to the x-axis and does not intersect the x-axis.
Number of zeroes = 0
(ii)
The curve intersects the x-axis at exactly one point.
Number of zeroes = 1
(iii)
The graph cuts the x-axis at three distinct points.
Number of zeroes = 3
(iv)
The graph is a parabola opening upward and touches the x-axis at one point.
Since it touches (but does not cut), it still counts as one zero.
Number of zeroes = 1
(v)
The graph intersects the x-axis at four distinct points.
Number of zeroes = 4
(vi)
The graph intersects the x-axis at three distinct points.
Number of zeroes = 3
Final Answers Summary
| Graph | Number of Zeroes |
|---|---|
| (i) | 0 |
| (ii) | 1 |
| (iii) | 3 |
| (iv) | 1 |
| (v) | 4 |
| (vi) | 3 |
Important Points to Remember
- Zeroes of a polynomial are the x-coordinates where the graph cuts the x-axis.
- If the graph touches the x-axis, it is still considered a zero.
- A polynomial of degree n can have at most n zeroes.