Mathematics — CBSE Class 10 board question

(d) $p(x)$ has at most three distinct zeroes.

A cubic polynomial (degree 3) can have at most 3 zeroes, as the graph of $y = p(x)$ intersects the x-axis at at most 3 points.

Source: Chapter 2, Section 2.2 & Summary Point 4

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• The key word is "at most" — a degree-3 polynomial can have 1, 2, or 3 zeroes (not necessarily exactly 3).
• Option (a) is wrong — "at most two" is too restrictive.
• Option (b) is wrong — it may have only one zero (e.g., $y = x^3$).
• Option (c) is wrong — "exactly three" is not always true.
• The general rule: a polynomial of degree $n$ has at most $n$ zeroes.