NCERT Mathematics · Class 10 · English · 2026-27

Polynomials — Exercise 2.1

Independently written, step-by-step solutions. Prompts below are concise paraphrases; use the official textbook for the complete question wording.

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Question 1

For each graph in NCERT Figure 2.10, count the distinct points where it meets the x-axis.

Step-by-step solution

A zero of p(x) is an x-coordinate for which p(x)=0. On a graph of y=p(x), count each distinct x-axis meeting point. A curve touching the axis also gives a zero; it need not cross through it.

Answer: (i) 0; (ii) 1; (iii) 3; (iv) 2; (v) 4; (vi) 3.

In (i), the graph stays above the axis. In (ii)–(v), count the crossings. In (vi), count the left crossing and the two separate points of contact: three in total.

Visual guide: The independently drawn diagrams below illustrate the same intersection counts. They are schematic patterns, not scale copies of the textbook graphs.

(i) No x-axis meeting point: 0 zeros.xy
(i) No x-axis meeting point: 0 zeros.
(ii) One x-axis meeting point: 1 zero.xy
(ii) One x-axis meeting point: 1 zero.
(iii) Three crossings: 3 zeros.xy
(iii) Three crossings: 3 zeros.
(iv) Two crossings: 2 zeros.xy
(iv) Two crossings: 2 zeros.
(v) Four crossings: 4 zeros.xy
(v) Four crossings: 4 zeros.
(vi) One crossing and two touches: 3 distinct zeros.xy
(vi) One crossing and two touches: 3 distinct zeros.

Resource ID: CB-10-M-CH2-EX2.1-Q1

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