Mathematics · Polynomials · NCERT Examples

Example 1

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Mathematics · Chapter 2 · NCERT Examples

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NCERT Example

Example 1

geometrical meaning of zeroes · polynomial graphs

Look at the graphs in Figure 2.9. Each is the graph of y = p(x), where p(x) is a polynomial. For each graph, find the number of zeroes of p(x).

Six polynomial graphs labelled i to vi, showing one, two, three, one, one and four x-axis intersections respectively. — Figure 2.9: six graphs of y = p(x).

Solution

The graph intersects the x-axis once, so it has 1 zero.
The graph intersects the x-axis twice, so it has 2 zeroes.
The graph intersects the x-axis three times, so it has 3 zeroes.
The graph intersects the x-axis once, so it has 1 zero.
The graph touches the x-axis once, so it has 1 zero.
The graph intersects the x-axis four times, so it has 4 zeroes.

Final answer

The numbers of zeroes are 1, 2, 3, 1, 1 and 4 respectively.