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Mathematics · Polynomials · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

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

  1. The graph intersects the x-axis once, so it has 1 zero.

  2. The graph intersects the x-axis twice, so it has 2 zeroes.

  3. The graph intersects the x-axis three times, so it has 3 zeroes.

  4. The graph intersects the x-axis once, so it has 1 zero.

  5. The graph touches the x-axis once, so it has 1 zero.

  6. 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.