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Graph of a polynomial… (Class 10 Maths Basic 2023, Q12)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 12

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQPolynomials

Graph of a polynomial p(x) is given in the figure. The number of zeroes of p(x) is:

  1. (A)2
  2. (B)3
  3. (C)4
  4. (D)5

Figure in the paper: Coordinate axes x'Ox and y'Oy. A curve rises from the left below the x-axis, crosses the x-axis on the negative side, peaks above the axis near the y-axis, dips to a trough above the x-axis, rises to a second peak, and then falls, crossing the x-axis on the positive side. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

Zeroes correspond to where the graph touches or cuts the x-axis.

Hint 2

Turning points above the axis do not count.

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. Zeroes are the x-coordinates where the graph meets the x-axis. The curve crosses the x-axis once on the negative side and once on the positive side; the trough stays above the axis.

  2. Number of zeroes = 2. Option (A).

    1 mark

Answer: 2, option (A)

Where the marks are

  • Counts the points where the graph meets the x-axis: 2 (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 paper2023 board paper, set 430/2/1 (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.