Vieta's might come in handy (Polynomials Sprint question)

Algebra Level 2

The roots of the equation

\[6x^3 - 3x^2 +2x - 1 = 0,\]

are \(\alpha, \beta\) and \(\gamma\). Find the value of

\[1 + \alpha + \beta + \gamma + \alpha \beta + \beta \gamma + \gamma \alpha + \alpha \beta \gamma. \]

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