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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 2.2 Geometrical Meaning of the Zeroes of a Polynomial § 2.3 Relationship between Zeroes and Coefficients of a Polynomial § 2.4 Summary
The zeroes of the polynomial $p(x) = x^2 + 4x + 3$ are given by:
  1. (a) $1, 3$
  2. (b) $-1, 3$
  3. (c) $1, -3$
  4. (d) $-1, -3$
Previously asked in CBSE board exam
2023 30/2/1 Q14
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer

(d) $-1, -3$

Factorising: $x^2 + 4x + 3 = (x+1)(x+3) = 0 \Rightarrow x = -1$ or $x = -3$.

Source: Chapter 2, Section 2.3

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Explanation

Factorise by splitting the middle term: $4x = 3x + x$, giving $(x+1)(x+3)$. Setting each factor to zero gives both zeroes as negative. A common mistake is ignoring the signs — since all coefficients are positive, both zeroes must be negative, ruling out options (a), (b), and (c) immediately.

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