The equation
\(x^{4}+x^{3}+c x^{2}+4 x-2=0,\)
where \(c\) is a constant, has roots \(\alpha, \beta, \gamma, \delta\).
(i) Use the substitution \(y=\frac{1}{x}\) to find an equation which has roots \(\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}, \frac{1}{\delta}\).

(ii) Find, in terms of \(c\), the values of \(\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2}\) and \(\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}+\frac{1}{\gamma^{2}}+\frac{1}{\delta^{2}}\).

(iii) Hence find
\(\left(\alpha-\frac{1}{\alpha}\right)^{2}+\left(\beta-\frac{1}{\beta}\right)^{2}+\left(\gamma-\frac{1}{\gamma}\right)^{2}+\left(\delta-\frac{1}{\delta}\right)^{2}\)
in terms of \(c\).

(iv) Deduce that when \(c=-3\) the roots of the given equation are not all real.