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
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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.