Symmetrical Quadratics!

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:

\[\huge{\color{Purple}{{a+b+c+d}}}\]

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