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

Q1. [1] § 2.3 Relationship between Zeroes and Coefficients of a Polynomial
If the zeroes of the polynomial $ax^2 + bx + \frac{2a}{b}$ are reciprocal of each other, then the value of b is
  1. A 2
  2. B $\frac{1}{2}$
  3. C $-2$
  4. D $-\frac{1}{2}$
Previously asked in CBSE board exam
2025 30/6/1 Q4
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Option A: 2

If zeroes are reciprocal, their product = 1. Product of zeroes = $\dfrac{2a/b}{a} = \dfrac{2}{b} = 1$, so b = 2.

Source: Chapter 2, Section 2.3

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Explanation

When zeroes are reciprocals of each other (say α and 1/α), their product = 1. Using the formula: product of zeroes = constant term ÷ coefficient of x², set $\frac{2a/b}{a} = \frac{2}{b} = 1$, giving b = 2. Don't confuse the constant term here — it is $\frac{2a}{b}$, not just 2.

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