# Cubic Roots

Algebra Level 4

Let $$x=a$$, $$y=b$$ and $$z=c$$ be the solutions of the simultaneous equations \begin{align} x+y+z &= -71, \\ 4x+2y+z &= -32, \\ 9x+3y+z &= -27. \end{align} Then the three roots of the cubic equation $$t^3+at^2+bt+c=0$$ are $$\alpha$$, $$\beta$$ and $$\gamma$$, where $$\alpha< \beta< \gamma$$. What is the value of $$100\alpha+10\beta+\gamma$$?

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