Polynomial Vieta

Algebra Level 2

The roots of the polynomial equation \( x^3 + 2 x^2 + 3 x + 4 = 0 \) are \( \alpha, \beta,\) and \(\gamma\). What is the value of

\[ \frac{ \alpha + \beta} { \gamma} + \frac{ \beta + \gamma} { \alpha } + \frac{ \gamma + \alpha } { \beta } ?\]

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