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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.
464993_09619211e71d4d8a9e7d2875e498ac56.png

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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).

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