Find the product of zeroes of the quadratic polynomial `x^(2)-2x-8.`

Explanation

To find the product of the zeroes of the quadratic polynomial \( p(x) = x^2 - 2x - 8 \), we can use Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.

### Step-by-Step Solution:

1. **Identify the coefficients**:
The given polynomial is \( p(x) = x^2 - 2x - 8 \). Here, we can identify the coefficients:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -2 \) (coefficient of \( x \))
- \( c = -8 \) (constant term)

2. **Use Vieta's formulas**:
According to Vieta's formulas, for a quadratic polynomial of the form \( ax^2 + bx + c \):
- The sum of the roots (zeroes) \( \alpha + \beta = -\frac{b}{a} \)
- The product of the roots (zeroes) \( \alpha \beta = \frac{c}{a} \)

3. **Calculate the product of the zeroes**:
Using the formula for the product of the roots:
\[ \alpha \beta = \frac{c}{a} = \frac{-8}{1} = -8 \]

4. **Conclusion**:
Therefore, the product of the zeroes of the polynomial \( x^2 - 2x - 8 \) is \( -8 \).

### Final Answer:
The product of the zeroes of the polynomial \( x^2 - 2x - 8 \) is \( -8 \).