Class 10 NCERT Solutions- Chapter 2 Polynomials - Exercise 2.1

Question 1. 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.

Solution:

So, we have equation y = p(x). When p(x) = 0, y = 0. 

That means we only need to find the number of times we get y = 0 in the graph.

In other words, the number of times the graph intersects the x-axis is the answer.

(i) 0. Because the graph doesn't intersect the x-axis.

(ii)1. Because the graph intersects the x-axis only at one point.

(iii) 3. Because the graph intersects the x-axis at three points.

(iv)2. Because the graph intersects the x-axis at two points.

(v)4. Because the graph intersects the x-axis at four points.

(vi) 3. Because the graph intersects the x-axis at three points.

Summary

Exercise 2.1 of NCERT Class 10 Chapter 2 - Polynomials focuses on the geometrical meaning of the zeroes of a polynomial. It introduces students to the concept that the zeroes of a polynomial are the x-coordinates of the points where the graph of the polynomial function y = f(x) intersects the x-axis. The exercise emphasizes understanding how to find and interpret zeroes graphically, and how the degree of a polynomial relates to the maximum number of zeroes it can have.