Q1. [1] § 2.2 Geometrical Meaning of the Zeroes of a Polynomial § 2.4 Summary
Directions: Two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (a), (b), (c) and (d).
Assertion (A) : The polynomial $p(y) = y^2 + 4y + 3$ 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.
Previously asked in CBSE board exam
2026 30/1/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$p(y) = y^2 + 4y + 3 = (y+1)(y+3)$ has two zeroes: $y = -1$ and $y = -3$, consistent with the fact that a quadratic polynomial has at most two zeroes.
Source: Chapter 2, Sections 2.2 and 2.4
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Explanation
- A is true: Factorising gives two distinct zeroes (–1 and –3).
- R is true: As stated in the NCERT summary (point 4), a quadratic polynomial can have at most 2 zeroes.
- R correctly explains A: The reason why p(y) has exactly two zeroes is precisely because it is a degree-2 (quadratic) polynomial, which can have at most 2 zeroes. Since it factors into two distinct linear factors, it achieves that maximum.
- Choose (a) when both statements are true AND the Reason directly justifies the Assertion.
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