\(f(x)\) is a monic quartic polynomial.

Such that

\(f(1)=-48\)

\(f(2)=0\)

\(f(3)=192\)

\(f(x)\) has real integer roots **\(\alpha\)** , **\(\beta\)** , **\(\gamma\)** and **\(\delta\)** and also integer coefficients .

Then find ,

**[\(\left ( \alpha^{4} + \beta^{4} + \gamma^{4}+ \delta^{4}\right )\)** + **\(\left ( \alpha^{3} + \beta^{3} + \gamma^{3}+ \delta^{3}\right )\)]** **mod** **11**

**This problem is original**

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