Assertion (A): The polynomial p(y) = y² + 4y + 3 has two zeroes. Reason (R): A quadratic polynomial can have at most two zeroes. (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2026: question 20

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedPolynomials

Assertion (A): The polynomial $p (y) = y^{2} + 4 y + 3$ has two zeroes.

Reason (R): A quadratic polynomial can have at most two zeroes.

(a)Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b)Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c)Assertion (A) is true, but Reason (R) is false.
(d)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/1/1.

Hints

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

Hint 1

Factorise $y^{2} + 4 y + 3$ .

Hint 2

Does 'at most two' guarantee 'exactly two'?

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.

$y^{2} + 4 y + 3 = (y + 1) (y + 3)$ , so the zeroes are $- 1$ and $- 3$ . Assertion is true.
A polynomial of degree 2 has at most 2 zeroes, so Reason is true. However, R only gives an upper limit; it does not explain why this polynomial actually has two zeroes. So R is not the correct explanation of A. Option (b).
1 mark

Answer: Option (b)

Where the marks are

Finds both statements true but R not explaining A, option (b) (1 mark)

Revise the chapter

Chapter: Polynomials (notes, formulas, where marks are lost and every past question)
Topic: Forming a Quadratic Polynomial from Its Zeros

Practise this chapterBoard-style questions from Polynomials, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/1/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 20

Hints

Step-by-step solution

Revise the chapter

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