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Mathematics — CBSE Class 10 board question

Q1. [1]
The number of quadratic polynomials having zeroes $-5$ and $-3$ is
  1. A 1
  2. B 2
  3. C 3
  4. D more than 3
Previously asked in CBSE board exam
2023 30/6/1 Q3
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

Answer: D — more than 3

A quadratic polynomial with zeroes −5 and −3 is of the form $k(x+5)(x+3)$, i.e., $k(x^2+8x+15)$, where $k$ is any non-zero real constant. Since $k$ can take infinitely many values, more than 3 such polynomials exist.

Source: Chapter 2, Section 2.3

Explanation

The key idea is that fixing the zeroes fixes only the ratio of coefficients, not the polynomial uniquely. Any scalar multiple $k \neq 0$ gives a different polynomial with the same zeroes. Examiners expect students to recall the form $k(x-\alpha)(x-\beta)$ and conclude that infinitely many (more than 3) such polynomials are possible.

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