The zeroes of a polynomial p(x) are precisely the x-coordinates of the points, where the graph of y=p(x) intersects the:

Options

A. x-axis
B. y-axis
C. origin
D. none of these

Answer

To solve the question, we need to understand what the zeros of a polynomial represent in the context of its graph.

### Step-by-Step Solution:

1. **Understanding the Polynomial**: A polynomial \( p(x) \) is a mathematical expression that can be represented as \( p(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 \), where \( a_n, a_{n-1}, ..., a_0 \) are constants and \( n \) is a non-negative integer.

2. **Definition of Zeros**: The zeros of the polynomial \( p(x) \) are the values of \( x \) for which \( p(x) = 0 \). In other words, these are the solutions to the equation \( p(x) = 0 \).

3. **Graphical Interpretation**: When we graph the polynomial \( p(x) \), the points where the graph intersects the x-axis are the points where the output (y-value) is zero. This means that at these points, the polynomial evaluates to zero.

4. **Identifying the Intersection**: The x-coordinates of the points where the graph intersects the x-axis correspond to the zeros of the polynomial. Therefore, if \( p(x) \) intersects the x-axis at a point \( (a, 0) \), then \( p(a) = 0 \).

5. **Conclusion**: Thus, the zeros of the polynomial \( p(x) \) are precisely the x-coordinates of the points where the graph of \( y = p(x) \) intersects the x-axis.

### Final Answer:
The zeros of a polynomial \( p(x) \) are precisely the x-coordinates of the points where the graph of \( y = p(x) \) intersects the **x-axis**.