The equation \(x^4 - x^2 + 2x + 5 = 0\) has roots \(\alpha, \beta, \gamma, \delta\).

(a) Find a quartic equation whose roots are \(\alpha^2, \beta^2, \gamma^2, \delta^2\) and state the value of \(\alpha^2 + \beta^2 + \gamma^2 + \delta^2\).

(b) Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} + \frac{1}{\delta^2}\).

(c) Find the value of \(\alpha^4 + \beta^4 + \gamma^4 + \delta^4\).