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Question:

The graphs of y=p(x) are given in the figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Solution:

(i) The graph does not intersect the x-axis, so there are no zeros in p(x) (ii) The graph intersects the x-axis at one place, so here there is one zero in p(x) (iii) The graph intersects the x-axis at three places, so that there are three zeros in p(x) (iv) The graph intersects the x-axis at two places, so here there are two zeros in p(x) (v) The graph intersects the x-axis at four places, so there are four zeros in p(x) (vi) The graph intersects the x-axis at three places, so that there are three zeros in p(x).