Given the quadratic equation \(3x^2 + 5x - 2 = 0\), let's first find the roots (\(\alpha\) and \(\beta\)) using the quadratic formula:

The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions are given by:

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

In this case, \(a = 3\), \(b = 5\), and \(c = -2\). Plugging in these values:

\[\alpha = \frac{-5 + \sqrt{5^2 - 4 \cdot 3 \cdot (-2)}}{2 \cdot 3} = \frac{-5 + \sqrt{49}}{6} = \frac{-5 + 7}{6} = \frac{2}{6} = \frac{1}{3}\]

\[\beta = \frac{-5 - \sqrt{5^2 - 4 \cdot 3 \cdot (-2)}}{2 \cdot 3} = \frac{-5 - \sqrt{49}}{6} = \frac{-5 - 7}{6} = \frac{-12}{6} = -2\]

Now, we need to find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\):

\[\frac{1}{\alpha} + \frac{1}{\beta} = \frac{1}{\frac{1}{3}} + \frac{1}{-2} = 3 - \frac{1}{2} = \frac{5}{2}\]

Therefore, the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is \(\frac{5}{2}\).