Q. 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:
We can reach the solution easily by understanding the statement of the question.
As the graphs of y = p(x) are given, and we have to find the number of zeroes of p(x), in each case, look at the graphs and visually find how many points the graph cuts or touches the x-axis.
The number of points it cuts or touches the x-axis are the zeroes of the polynomial p(x).
(i) The number of zeroes is 0 as the graph doesn’t cut the x-axis at any point.
(ii) The number of zeroes is 1 as the graph cuts the x-axis at only one point.
(iii) The number of zeroes is 3 as the graph cuts the x-axis at 3 points.
(iv) The number of zeroes is 2 as the graph cuts the x-axis at 2 points.
(v) The number of zeroes is 4 as the graph cuts the x-axis at 4 points.
(vi) The number of zeroes is 3 as the graph cuts the x-axis at 3 points.