Algebra Level 4

Let $$a$$ and $$b$$ be the roots of the quadratic equation $$x^2-100cx-101d=0$$.

Let $$c$$ and $$d$$ be the roots of the quadratic equation $$x^2-100ax-101b=0$$.

If $$a,b,c$$ and $$d$$ are distinct, non zero real numbers, then find the value of:

$\huge{\color{Purple}{{a+b+c+d}}}$

×