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NCERT Solutions · Class 10 · Chapter 2: Polynomials

NCERT Solutions for Class 10 Maths Chapter 2 Exercise 2.1

Exercise 2.1: Number of zeroes from a graph. The zeroes of \(p(x)\) are the x-coordinates of the points where the graph of \(y = p(x)\) meets the x-axis. Count the meeting points (touching counts too).

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Exercise 2.1 questions and solutions

Exercise 2.1, Question 1

The textbook shows six graphs of \(y = p(x)\). Find the number of zeroes of \(p(x)\) in each.
(i) The graph does not meet the x-axis at all.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(0\) zeroes
(ii) The graph meets the x-axis at exactly one point.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(1\) zero
(iii) The graph meets the x-axis at three points.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(3\) zeroes
(iv) The graph meets the x-axis at two points.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(2\) zeroes
(v) The graph meets the x-axis at four points.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(4\) zeroes
(vi) The graph meets the x-axis at three points.
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  1. Count the points where the graph meets (crosses or touches) the x-axis.
Answer: \(3\) zeroes

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Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.