\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).
Answer Details
The sum of the roots of a quadratic equation of the form \(ax^{2} + bx + c = 0\) is given by \(-\frac{b}{a}\).
In this case, the given quadratic equation is \(2x^{2} - 3x + 4 = 0\). Therefore, the sum of the roots, \(\alpha\) and \(\beta\), is given by \(-\frac{-3}{2} = \frac{3}{2}\).
Hence, the answer is \(\frac{3}{2}\), which represents the sum of the roots of the given quadratic equation.