If one zero of the polynomial $p(x) = 6x^2 + 37x - (k - 2)$ is reciprocal of the other, then find the value of $k$.

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Step 1: Let the zeroes be $\alpha$ and $\frac{1}{\alpha}$. Product of zeroes $= \alpha \cdot \frac{1}{\alpha} = 1 = \frac{-(k-2)}{6}$
Step 2: $6 = -(k - 2) \Rightarrow 6 = -k + 2 \Rightarrow k = -4$

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