Roots of a Quartic

Algebra Level 3

\[ \large f(x)^2+3f(x)+2\]

If \(f(x)= x^2-8x\), then the equation above has 4 distinct, real roots of the form \(4 \pm{\sqrt{a}}\) for real value \(a\).

Denote the sum of all values of \(a\) as \(S\). Evaluate \( \frac {1740}S \).

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