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The graph of y = p(x) is given… (Class 10 Maths 2023, Q1)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 1

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQPolynomials

The graph of is given, for a polynomial . The number of zeroes of from the graph is

  1. (A)3
  2. (B)1
  3. (C)2
  4. (D)0

Figure in the paper: Coordinate axes x'Ox and y'Oy. A downward-opening parabola-shaped curve labelled y = p(x) touches the x-axis at one point (its vertex lies on the x-axis just to the right of O) and cuts the y-axis below O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Zeroes of are the -values where .

Hint 2

Count how many times the curve meets the -axis. Touching it also counts.

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 of equals the number of points where the graph of meets the -axis.

  2. The downward-opening curve touches the -axis at exactly one point, its vertex. It does not cross the -axis anywhere else.

  3. So has exactly 1 zero. Option (B).

    1 mark

Answer: 1, option (B)

Where the marks are

  • Counts one point of contact with the x-axis, so 1 zero, option (B) (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 30/1/1 (Standard): 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.