Roots of a Quartic

Algebra Level 3

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

If f(x)=x28xf(x)= x^2-8x, then the equation above has 4 distinct real roots of the form 4±a4 \pm{\sqrt{a}} for real value aa.

Denote the sum of all values of aa as SS. Evaluate 1740S \dfrac {1740}S .

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