The product of all the solutions to the equation `3y ^(2)+4v -2 =0` is M. What is the value of M ?

Options

A. `-3`
B. `-2/3`
C. `-1/3`
D. `4/3`

Explanation

To find the product of all the solutions to the quadratic equation \(3y^2 + 4y - 2 = 0\), we can use the relationship between the coefficients of the quadratic equation and its roots.

### Step-by-Step Solution:

1. **Identify the coefficients**: In the quadratic equation \(3y^2 + 4y - 2 = 0\), we can identify the coefficients as follows:
- \(a = 3\) (coefficient of \(y^2\))
- \(b = 4\) (coefficient of \(y\))
- \(c = -2\) (constant term)

2. **Use the product of roots formula**: The product of the roots of a quadratic equation \(ax^2 + bx + c = 0\) is given by the formula:
\[ \text{Product of roots} = \frac{c}{a} \]

3. **Substitute the values of \(c\) and \(a\)**:
- Here, \(c = -2\) and \(a = 3\).
- Therefore, the product of the roots \(M\) can be calculated as:
\[ M = \frac{c}{a} = \frac{-2}{3} \]

4. **Final answer**: Thus, the value of \(M\) is:
\[ M = -\frac{2}{3} \]