If the product of the zeros of the polynomial `ax^(2)-6x-12` is 4 , then find the value of 'a' .

Answer

To find the value of 'a' given that the product of the zeros of the polynomial \( ax^2 - 6x - 12 \) is 4, we can follow these steps:

### Step 1: Identify the general form of a quadratic polynomial
The general form of a quadratic polynomial is given by:
\[ ax^2 + bx + c = 0 \]
In our case, the polynomial is \( ax^2 - 6x - 12 \), where \( a \) is the coefficient of \( x^2 \), \( b = -6 \), and \( c = -12 \).

### Step 2: Use the formula for the product of the zeros
The product of the zeros (or roots) of a quadratic polynomial \( ax^2 + bx + c \) is given by:
\[ \text{Product of zeros} = \frac{c}{a} \]
For our polynomial, this becomes:
\[ \text{Product of zeros} = \frac{-12}{a} \]

### Step 3: Set up the equation based on the given product of zeros
According to the problem, the product of the zeros is given as 4. Therefore, we can set up the equation:
\[ \frac{-12}{a} = 4 \]

### Step 4: Solve for 'a'
To find 'a', we can rearrange the equation:
\[ -12 = 4a \]
Now, divide both sides by 4:
\[ a = \frac{-12}{4} \]
Simplifying this gives:
\[ a = -3 \]

### Conclusion
Thus, the value of \( a \) is:
\[ \boxed{-3} \]

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