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

Q1. [1] § 2.2 Geometrical Meaning of the Zeroes of a Polynomial § 2.4 Summary
The graph of $y = f(x)$ is given. The number of distinct zeroes of $y = f(x)$ is :
  1. A 0
  2. B 1
  3. C 2
  4. D 3
Previously asked in CBSE board exam
2026 30/2/1 Q4
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Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer

Option C: 2

The curve crosses the x-axis at point A (one zero) and touches (is tangent to) the x-axis at one point to the right of O (one zero). Total distinct zeroes = 2.

Explanation

A zero is the x-coordinate of a point where the graph meets the x-axis. Crossing counts as one zero; touching (tangent) also counts as one zero (a repeated root, but still one distinct zero). So crossing at A + touching at one point = 2 distinct zeroes. Examiners expect you to distinguish "crosses" (1 zero) from "touches" (1 zero, repeated) and count distinct contact points with the x-axis.

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