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

Q1. [1] § 2.3 Relationship between Zeroes and Coefficients of a Polynomial § 2.4 Summary
If the zeroes of the quadratic polynomial $x^2 + (a + 1)x + b$ are 2 and $-3$, then
  1. A $a = -7, b = -1$
  2. B $a = 5, b = -1$
  3. C $a = 2, b = -6$
  4. D $a = 0, b = -6$
Previously asked in CBSE board exam
2023 30/6/1 Q17
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Option D: $a = 0, b = -6$

Sum of zeroes = $2 + (-3) = -1 = -(a+1)$, so $a+1 = 1 \Rightarrow a = 0$.
Product of zeroes = $2 \times (-3) = -6 = b$, so $b = -6$.

Source: Chapter 2, Section 2.3

Explanation

Use the relations: sum of zeroes $= \frac{-(a+1)}{1}$ and product of zeroes $= \frac{b}{1}$. Plug in zeroes 2 and −3 to get both values directly. Watch out for option C ($a=2, b=-6$) — it has the correct $b$ but wrong $a$, a common trap.

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