Question 1
The graphs of y = p(x) are given in Fig below, for some polynomials p(x). Find the
number of zeroes of p(x), in each case.
Solution:
Graphical method to find zeroes:
Total number of zeroes in any polynomial equation = total number of times the curve intersects x-axis.
(i) The number of zeroes is 0 as the graph doesn’t cuts 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.