The product of cube roots of –1 is equal :

Options

A. 0
B. 1
C. `-1`
D. None of these

Answer

To solve the problem of finding the product of the cube roots of -1, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
We start by expressing the problem mathematically. We need to find the cube roots of -1. We can write this as:
\[ z^3 = -1 \]

2. **Rewrite the Equation**:
We can rewrite the equation as:
\[ z^3 + 1 = 0 \]

3. **Identify Coefficients**:
In the polynomial \( z^3 + 1 = 0 \), we can identify the coefficients:
- \( a = 1 \) (coefficient of \( z^3 \))
- \( d = 1 \) (constant term)

4. **Use the Product of Roots Formula**:
The product of the roots of a polynomial \( ax^3 + bx^2 + cx + d = 0 \) is given by:
\[ \text{Product of roots} = -\frac{d}{a} \]
In our case, substituting the values we have:
\[ \text{Product of roots} = -\frac{1}{1} = -1 \]

5. **Conclusion**:
Therefore, the product of the cube roots of -1 is:
\[ -1 \]

### Final Answer:
The product of the cube roots of -1 is **-1**.

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