The polynomial `p(x)=ax^(2)+bx+c` can have at most zeros, where `ane0`:

Options

A. One
B. Two
C. Three
D. None of these.

Explanation

To determine the maximum number of zeros (or roots) of the polynomial \( p(x) = ax^2 + bx + c \), where \( a \neq 0 \), we follow these steps:

### Step-by-Step Solution:

1. **Identify the Type of Polynomial**:
The given polynomial is \( p(x) = ax^2 + bx + c \). This is a quadratic polynomial because the highest power of \( x \) is 2.

2. **Understand the Degree of the Polynomial**:
The degree of a polynomial is defined as the highest power of the variable \( x \) in the polynomial. In this case, the highest power of \( x \) is 2 (from the term \( ax^2 \)).

3. **Determine the Maximum Number of Zeros**:
A polynomial of degree \( n \) can have at most \( n \) zeros. Since our polynomial is of degree 2, it can have at most 2 zeros.

4. **Conclusion**:
Therefore, the polynomial \( p(x) = ax^2 + bx + c \) can have at most 2 zeros.

### Final Answer:
The polynomial \( p(x) = ax^2 + bx + c \) can have at most 2 zeros.