# 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.