If $\alpha$ and $\beta$ are the roots of $2x^2 - 3x + 1 = 0$, find the value of $\alpha^2 + \beta^2$.

For $ax^2 + bx + c = 0$, $\alpha + \beta = -\dfrac{b}{a} = \dfrac{3}{2}$ and $\alpha\beta = \dfrac{c}{a} = \dfrac{1}{2}$. Then $\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \dfrac{9}{4} - 1 = \dfrac{5}{4}$. Forgetting to subtract $2\alpha\beta$ leaves $\dfrac{9}{4}$; adding it instead gives $\dfrac{13}{4}$.