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If zeroes of the… (Class 10 Maths SQP 2025-26, Q12)

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

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 12

From the official CBSE sample question paper for 2025-26, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQPolynomials

If zeroes of the quadratic polynomial (a, c ≠0) are equal, then

  1. (A)c and b must have opposite signs
  2. (B)c and a must have opposite signs
  3. (C)c and b must have same signs
  4. (D)c and a must have same signs

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

What is the condition on the discriminant for equal roots?

Hint 2

Is positive or negative?

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. Equal zeroes means the discriminant is zero: , so .

  2. Since , , so and hence . Therefore a and c have the same sign, which is option (D).

    1 mark

Answer: Option (D)

Where the marks are

  • Uses to deduce , so a and c have the same sign, option (D) (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 (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.