I and Phi?

Algebra Level 5

\[\large 210+315\phi+76i\phi^3x+34\phi^2x^2+4i\phi x^3+x^4=0\]

The equation above has 4 distinct roots \(a_n\) for \(n={1,2,3,4}\) where \(|a_1|<|a_2|<|a_3|<|a_4|\).

Find the value of \(\dfrac{a_1+a_2-a_3}{a_4}\).

Details and assumptions:

\(i=\sqrt{-1}\), \(\phi=\dfrac{1+\sqrt5}{2}\) .

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