The graph of a polynomial crosses the x-axis at two distinct points and does not merely touch it at any point. What does this imply?

There are two distinct real zeroes

If the graph crosses the x-axis at two distinct points, each crossing corresponds to a different real root of the polynomial. Crossing typically indicates an odd multiplicity (often 1) at that root. Choice B is incorrect because a repeated root refers to the same x-value occurring multiple times (leading to touching or flattened behavior at one point), not two separate intersection points. C and D are clearly wrong: no real roots would give no intersections, and every point being a root would mean the polynomial is identically zero. Exam tip: count distinct intersection x-values for number of distinct real roots; check whether the graph crosses (odd multiplicity) or merely touches (even multiplicity).

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..