# A Crazy Quartic

Level pending

Let $$a,b,c,d$$ be the roots of the following equation.

$$$$x^4+10x^3+kx^2+100x-1001=0$$$$

If $$ab=77$$, the value of $$k$$ can be expressed as a mixed number $$p\frac{q}{r}$$, where $$p$$ is a positive integer, and $$q$$ and $$r$$ are coprime positive integers. Find the value of $$p+q+r$$.

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