Number of solutions to $f(x)\equiv 0 \mod(11\cdot 19^{2})$

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I have been asked to explain why the number of solutions of the polynomial congruence $f(x)\equiv 0 \mod (11\cdot 19^{2})$ cannot be 121, where $f(x)=x^{10}+10x^{8}-17x+12$.

Any ideas?