The graph of p(x) = 3x — 2 — x² intersects the X-axis in _____ points.

The zeros of p(x) are the intersections points of the equation, p(x) = 3x – 2 – x² with the x-axis.

∴ The number of distinct zeros of p(x) gives the number of distinct intersection points on the X-axis.

To find the zeros of p(x), consider p(x) = 0

∴3x – 2 – x² = 0

∴ x² – 3x+ 2 = 0

∴ x² – x – 2x+ 2 = 0

∴ x(x – 1) – 2(x – 1) = 0

∴ (x – 1)(x – 2) = 0

∴ x = 1 or x = 2 are the zeros of p(x).

⇒The graph of p(x) intersects X-axis at two points.

The correct option is C.