India Site

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.

Solutions:

The following is a graphical way for finding zeroes:-

When solving any polynomial equation, the total number of zeroes equals the total number of times the curve meets the x-axis.

i) The number of zeroes in p(x) is zero in the provided graph since the graph is parallel to the x-axis and does not cut it at any point.

(ii) The number of zeroes in p(x) is one in the given graph because the graph contacts the x-axis at just one location in the given graph.

(iii) In the given graph, the number of zeroes in the function p(x) equals 3, which indicates that the graph crosses the x-axis at any three locations.

(iv) As a result, there are two spots on the graph where the x-axis meets the graph, resulting in a total of two zeroes for p(x).

(v) The number of zeroes in p(x) is four in the above graph because the graph meets the x-axis at four spots.

(vi) p(x) has three zeroes in the given graph because the graph meets the x-axis at three points, which results in the number of zeroes being 3.