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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
The zeroes of the quadratic polynomial $2x^2 - 3x - 9$ are :
  1. A $3, \dfrac{-3}{2}$
  2. B $-3, \dfrac{3}{2}$
  3. C $-3, \dfrac{-3}{2}$
  4. D $3, \dfrac{3}{2}$
Previously asked in CBSE board exam
2024 30/3/1 Q6
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Model Answer

Option A: $3, \dfrac{-3}{2}$

Factorising: $2x^2 - 3x - 9 = 2x^2 - 6x + 3x - 9 = 2x(x-3) + 3(x-3) = (x-3)(2x+3)$

Zeroes: $x = 3$ or $x = -\dfrac{3}{2}$

Source: Chapter 2, Section 2.3

Explanation

Split the middle term $-3x$ as $-6x + 3x$ (product = $2 \times (-9) = -18$, sum = $-3$). After factorising, set each factor to zero. Examiners expect the factorisation step shown — don't just state the answer for a calculation-based MCQ if working is expected.

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