Find the product of zeroes of the quadratic polynomial `3x^(2)-x-4.`

Answer

To find the product of the zeroes of the quadratic polynomial \(3x^2 - x - 4\), we can follow these steps:

### Step 1: Identify the coefficients
The general form of a quadratic polynomial is given by:
\[ ax^2 + bx + c \]
For the polynomial \(3x^2 - x - 4\), we can identify the coefficients:
- \(a = 3\)
- \(b = -1\)
- \(c = -4\)

### Step 2: Use the formula for the product of the zeroes
The product of the zeroes (roots) of a quadratic polynomial can be calculated using the formula:
\[ \text{Product of zeroes} = \frac{c}{a} \]
where \(c\) is the constant term and \(a\) is the coefficient of \(x^2\).

### Step 3: Substitute the values into the formula
Now, substituting the values of \(c\) and \(a\) into the formula:
\[ \text{Product of zeroes} = \frac{-4}{3} \]

### Step 4: Write the final answer
Thus, the product of the zeroes of the quadratic polynomial \(3x^2 - x - 4\) is:
\[ \text{Product of zeroes} = -\frac{4}{3} \]