Quadratic equation biting its own tail

Algebra Level 5

Find the number of integer quadruples (a,b,c,d)(a,b,c,d) where a,b,ca, b, c and dd are between 0 and 100 inclusive, such that aa and bb are the roots of the quadratic equation x2cx+d=0,x^2-cx+d=0, while cc and dd are the roots of the quadratic equation x2ax+b=0.x^2-ax+b=0.

Details and assumptions

The roots are counted with multiplicity.

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