The graph of $y = p(x)$ is given, for a polynomial $p(x)$. The number of zeroes of $p(x)$ from the graph is

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## Model Answer **Answer: (B) 1** The parabola touches the x-axis at exactly one point, so the number of zeroes of p(x) is **1**. *Source: Chapter 2, Section 2.2 — Geometrical Meaning of the Zeroes of a Polynomial* --- ## Explanation The number of zeroes equals the number of points where the graph of y = p(x) intersects (or touches) the x-axis. A parabola that **touches** the x-axis at exactly one point (two coincident points — Case ii) gives **one zero** (repeated). If the graph lay entirely below the x-axis without touching, the answer would be 0. Students often confuse "touches" with "no zero" — touching still counts as one zero.

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