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.

NCERT Solutions Class 10 Maths Chapter 2 Ex2.1 Q1. Sol

Solution:

Graphical method to find zeroes:-

Total number of zeroes in any polynomial equation = Total number of times the curve intersects the x-axis.

(i) The graph is parallel to x-axis does not cut it at any point.

Thus, the number of zeroes of p(x) = 0

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

Thus, the number of zeroes of p(x) = 1

(iii) The graph intersects the x-axis at any three points.

Thus, the number of zeroes of p(x) = 3

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

Thus, the number of zeroes of p(x) = 2

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

Thus, the number of zeroes of p(x) = 4

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

Thus, the number of zeroes of p(x) = 3