The maximum number of zeroes a cubic polynomial can have, is

Options

A. 1
B. 4
C. 2
D. 3

Answer

To determine the maximum number of zeros a cubic polynomial can have, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of a Cubic Polynomial**:
A cubic polynomial can be expressed in the standard form as:
\[ P(x) = Ax^3 + Bx^2 + Cx + D \]
where \(A\), \(B\), \(C\), and \(D\) are constants, and \(A \neq 0\).

2. **Identify the Degree of the Polynomial**:
The degree of a polynomial is the highest power of the variable \(x\) in the polynomial. In this case, the highest power of \(x\) is 3 (from the term \(Ax^3\)). Therefore, the degree of the polynomial \(P(x)\) is 3.

3. **Relate the Degree to the Number of Zeros**:
The Fundamental Theorem of Algebra states that a polynomial of degree \(n\) can have at most \(n\) real roots (or zeros). Since our polynomial is of degree 3, it can have at most 3 real zeros.

4. **Conclusion**:
Thus, the maximum number of zeros a cubic polynomial can have is:
\[ \text{Maximum number of zeros} = 3 \]

### Final Answer:
The maximum number of zeros a cubic polynomial can have is **3**.

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