The cubic equation \(2x^3 + x^2 - px - 5 = 0\), where \(p\) is a positive constant, has roots \(\alpha, \beta, \gamma\).

(a) State, in terms of \(p\), the value of \(\alpha\beta + \beta\gamma + \gamma\alpha\).

(b) Find the value of \(\alpha^2\beta\gamma + \alpha\beta^2\gamma + \alpha\beta\gamma^2\).

(c) Deduce a cubic equation whose roots are \(\alpha\beta, \beta\gamma, \alpha\gamma\).

(d) Given that \(\alpha^2 + \beta^2 + \gamma^2 = \frac{1}{3}\), find the value of \(p\).