Find the sum of and product of the roots of the equation ` 3x ^2 +2x -1=0`.

Answer

To find the sum and product of the roots of the quadratic equation \(3x^2 + 2x - 1 = 0\), we can follow these steps:

### Step 1: Identify the coefficients
The given quadratic equation is in the form \(ax^2 + bx + c = 0\). Here, we identify:
- \(a = 3\)
- \(b = 2\)
- \(c = -1\)

### Step 2: Use the formula for the sum of the roots
The sum of the roots (\(\alpha + \beta\)) of a quadratic equation is given by the formula:
\[ \alpha + \beta = -\frac{b}{a} \]
Substituting the values of \(b\) and \(a\):
\[ \alpha + \beta = -\frac{2}{3} \]

### Step 3: Use the formula for the product of the roots
The product of the roots (\(\alpha \beta\)) of a quadratic equation is given by the formula:
\[ \alpha \beta = \frac{c}{a} \]
Substituting the values of \(c\) and \(a\):
\[ \alpha \beta = \frac{-1}{3} \]

### Final Results
- The sum of the roots is \(-\frac{2}{3}\).
- The product of the roots is \(-\frac{1}{3}\).