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

Answer

To find the product of the zeros of the quadratic polynomial \( x^2 - 2x - 8 \), we can follow these steps:

### Step 1: Identify the coefficients
The given quadratic polynomial is \( x^2 - 2x - 8 \). We can identify the coefficients as follows:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -2 \) (coefficient of \( x \))
- \( c = -8 \) (constant term)

### Step 2: Use the formula for the product of the zeros
For a quadratic polynomial of the form \( ax^2 + bx + c \), the product of the zeros (roots) \( \alpha \) and \( \beta \) can be calculated using the formula:
\[ \alpha \cdot \beta = \frac{c}{a} \]

### Step 3: Substitute the values
Now, we can substitute the values of \( c \) and \( a \) into the formula:
\[ \alpha \cdot \beta = \frac{-8}{1} \]

### Step 4: Calculate the product
Calculating the above expression gives:
\[ \alpha \cdot \beta = -8 \]

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

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