\[\begin{eqnarray} abc+ab+bc+ca+a+b+c&=&1\\ bcd+bc+cd+db+b+c+d&=&7 \\ cda+cd+da+ac+c+d+a&=&2\\ dab+da+ab+bd+d+a+b&=&9 \end{eqnarray} \] There exists a monic quartic polynomial with non-real roots \(a,b,c,d\). Compute its discriminant.

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