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Graph of polynomial p(x)… (Class 10 Maths Basic 2025, Q1)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 1

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQPolynomials

In the given figure, graph of polynomial is shown. Number of zeroes of is

  1. (A)3
  2. (B)2
  3. (C)1
  4. (D)4

Figure in the paper: Graph of a cubic-shaped polynomial p(x) on x-x' and y-y' axes with origin O. The curve starts at the origin, rises to a maximum above the x-axis, crosses the x-axis, dips to a minimum below the x-axis, then rises again crossing the x-axis to the right of the minimum. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Zeroes are the points where the graph touches or cuts the x-axis.

Hint 2

Do not forget the origin itself.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. The number of zeroes equals the number of points where the graph meets the -axis.

  2. The curve meets the -axis at O, again after the maximum, and again after the minimum. That is 3 points, so has 3 zeroes.

    1 mark

Answer: 3, option (A)

Where the marks are

  • Counts the 3 points where the graph meets the x-axis (1 mark)

Revise the chapter

  • Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/6/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.