# 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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