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The number of polynomials having… (Class 10 Maths 2023, Q1)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 1

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, 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 number of polynomials having zeroes and is :

  1. (A)only one
  2. (B)infinite
  3. (C)exactly two
  4. (D)at most two

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Can you multiply a polynomial by a constant without changing its zeroes?

Hint 2

Write the polynomial as and ask how many values can take.

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. Any polynomial , , has zeroes and .

  2. Since can be any non-zero real number, there are infinitely many such polynomials. Option (B).

    1 mark

Answer: Infinite, option (B)

Where the marks are

  • Recognises that works for every (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 30/5/1 (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.