# 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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