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The number of… (Class 10 Maths Basic SQP 2025-26, Q3)

questionbuddy.in/q/cbse-10-maths-2025-26-sqp-basic-q3-number-polynomials-having-zeroes

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 3

From the official CBSE sample question paper for 2025-26, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQPolynomials

The number of polynomials having and as its zeroes is

  1. (A)one
  2. (B)two
  3. (C)three
  4. (D)Infinitely many

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Write one polynomial with these zeroes.

Hint 2

What happens if you multiply it by a constant?

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 with has zeroes and .

  2. Since can take infinitely many real values, there are infinitely many such polynomials, option (D).

    1 mark

Answer: Infinitely many, option (D)

Where the marks are

  • Recognises works for every non-zero (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 paperSample paper 2025-26 (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.