Polynomial Vieta

Algebra Level 2

The roots of the polynomial equation x3+2x2+3x+4=0 x^3 + 2 x^2 + 3 x + 4 = 0 are α,β, \alpha, \beta, and γ\gamma. What is the value of

α+βγ+β+γα+γ+αβ? \frac{ \alpha + \beta} { \gamma} + \frac{ \beta + \gamma} { \alpha } + \frac{ \gamma + \alpha } { \beta } ?

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