Find the sum of the zeroes of the quadratic polynomial `3x^2 + 5x - 2`.

Answer

To find the sum of the zeroes of the quadratic polynomial \(3x^2 + 5x - 2\), we can use the relationship between the coefficients of the polynomial and its zeroes.

### Step-by-step Solution:

1. **Identify the coefficients**:
The given quadratic polynomial is \(3x^2 + 5x - 2\). Here, we can identify the coefficients as follows:
- \(a = 3\) (coefficient of \(x^2\))
- \(b = 5\) (coefficient of \(x\))
- \(c = -2\) (constant term)

2. **Use the formula for the sum of the zeroes**:
The sum of the zeroes (let's denote them as \(\alpha\) and \(\beta\)) of a quadratic polynomial \(ax^2 + bx + c\) is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]

3. **Substitute the values of \(a\) and \(b\)**:
Now, substituting the values of \(b\) and \(a\) into the formula:
\[ \alpha + \beta = -\frac{5}{3} \]

4. **Final result**:
Thus, the sum of the zeroes of the polynomial \(3x^2 + 5x - 2\) is:
\[ -\frac{5}{3} \]

### Summary:
The sum of the zeroes of the quadratic polynomial \(3x^2 + 5x - 2\) is \(-\frac{5}{3}\).