(a) The quartic equation \(x^4+x^3+x^2+x+1=0\) has roots \(\alpha,\beta,\gamma,\delta\). Show that a quartic equation with roots \(2\alpha+1,2\beta+1,2\gamma+1,2\delta+1\) is \(y^4-2y^3+4y^2+2y+11=0\).

(b) The sum \((2\alpha+1)^n+(2\beta+1)^n+(2\gamma+1)^n+(2\delta+1)^n\) is denoted by \(S_n\). Find \(S_2\).

(c) Given that \(S_3=-22\), find \(S_4\).