Quadratic equation biting its own tail

Algebra Level 5

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

Details and assumptions

The roots are counted with multiplicity.

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