Mathematics
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.
Answer
We know that,
The number of points where the graph cuts the x-axis gives the number of zeroes of any polynomial p(x).
(i) In the figure,
The graph does not cuts x-axis.
Hence, there are no zeroes in this graph.
(ii) In the figure,
The graph cuts x-axis at a single point.
Hence, there is one zero in this graph.
(iii) In the figure,
The graph cuts x-axis at three points.
Hence, there are three zeroes in this graph.
(iv) In the figure,
The graph cuts x-axis at two points.
Hence, there are two zeroes in this graph.
(v) In the figure,
The graph cuts x-axis at four points.
Hence, there are four zeroes in this graph.
(vi) In the figure,
The graph cuts x-axis at three points.
Hence, there are three zeroes in this graph.
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