A Crazy Quartic

Level pending

Let \(a,b,c,d\) be the roots of the following equation.

\(\begin{equation} x^4+10x^3+kx^2+100x-1001=0 \end{equation}\)

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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