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Mathematics · Polynomials · NCERT Exercises

Exercise 2.1

Complete, independently verified solutions for NCERT Exercise 2.1.

Mathematics · Chapter 2 · NCERT Exercises

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Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

Question

Question 1

geometrical meaning of zeroes · polynomial graphs

The graphs of y = p(x) are given in Figure 2.10 for some polynomials p(x). Find the number of zeroes of p(x) in each case.

Six polynomial graphs labelled i to vi, showing zero, one, three, two, four and three x-axis intersections respectively.
Figure 2.10: graphs for Exercise 2.1.

Solution

  1. The graph does not meet the x-axis, so it has 0 zeroes.

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

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

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

  5. The graph meets the x-axis four times, so it has 4 zeroes.

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

Final answer

The numbers of zeroes are 0, 1, 3, 2, 4 and 3 respectively.