The graph of y = p(x) are given below, for some polynomial p(x). Find the number of zeroes of p(x), in each case.

Question : The graph of y = p(x) are given below, for some polynomial p(x). Find the number of zeroes of p(x), in each case.

polynomial graph

Solution :

(i)  There are no zeroes as the graph does not intersect the x-axis.

(ii)  The number of zeroes is one as the graph intersect the x-axis at one point only.

(iii)  The number of zeroes is three as the graph intersect the x-axis at three points.

(iv)  The number of zeroes is two as the graph intersect the x-axis at two points.

(v)  The number of zeroes is four as the graph intersect the x-axis at four points.

(vi)  The number of zeroes is three as the graph intersect the x-axis at three points.

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