1. The problem states that the roots of the quadratic equation $$2x^2 - 5x + m = 0$$ are $$\alpha$$ and $$\beta$$, and we need to find $$\alpha^2 + \beta^2$$ in terms of $$m$$. 2. Recall the sum and product of roots for a quadratic equation $$ax^2 + bx + c = 0$$ are: $$\alpha + \beta = -\frac{b}{a}$$ $$\alpha \beta = \frac{c}{a}$$ 3. For our equation, $$a=2$$, $$b=-5$$, and $$c=m$$, so: $$\alpha + \beta = -\frac{-5}{2} = \frac{5}{2}$$ $$\alpha \beta = \frac{m}{2}$$ 4. Use the identity: $$\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta$$ 5. Substitute the values: $$\alpha^2 + \beta^2 = \left(\frac{5}{2}\right)^2 - 2 \times \frac{m}{2} = \frac{25}{4} - m$$ 6. Therefore, the expression for $$\alpha^2 + \beta^2$$ in terms of $$m$$ is: $$\boxed{\frac{25}{4} - m}$$ 7. Comparing with the options given, the correct answer is (a) $$\frac{25}{4} - m$$.