# 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 $$\frac {1740}S$$.

×