If $\alpha$ and $\beta$ are the zeroes of the polynomial $x^2 + x - 2$, then find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.

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Step 1: $\alpha + \beta = -1$ and $\alpha\beta = -2$
Step 2: $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta} = \frac{(\alpha + \beta)^2 - 2\alpha\beta}{\alpha\beta}$
Step 3: $= \frac{(-1)^2 - 2(-2)}{-2} = \frac{1 + 4}{-2} = \frac{-5}{2}$

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