# Easy to think, Harder to solve

Algebra Level 5

$$f(x)$$ 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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