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 \( \dfrac {1740}S \).
by
Alex Delhumeau