1. The problem states that \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(2y^2 - 5y - 3 = 0\). We need to find the value of \(\alpha + \beta\). 2. Recall the sum of roots formula for a quadratic equation \(ay^2 + by + c = 0\) is given by: $$\alpha + \beta = -\frac{b}{a}$$ where \(a\), \(b\), and \(c\) are coefficients of the quadratic equation. 3. In our equation, \(a = 2\), \(b = -5\), and \(c = -3\). 4. Substitute these values into the formula: $$\alpha + \beta = -\frac{-5}{2} = \frac{5}{2}$$ 5. Therefore, the sum of the roots \(\alpha + \beta = \frac{5}{2}\).