# Devastating blow

Algebra Level 3

$\large x^{2011} + a_{1}x^{2010} + a_{2} x^{2009} +\ldots + a_{2010} +1$

Given $x_1 , x_2 , x_3 , \ldots , x_{2011}$ are the roots of the polynomial above and that \begin{aligned} y_1 &=& x_{1} \ x_{2} \cdots x_{10} \\ y_2 &=& x_{2} \ x_{3} \cdots x_{11} \\ y_3 &=& x_{3} \ x_{4} \cdots x_{12} \\ &\cdot& \\ &\cdot& \\ &\cdot& \\ y_{2011} &=& x_{2011}\ x_{1} \ x_{2} \cdots x_{9} \end{aligned}

Find the value of ${{(y_1 \ y_2\ldots y_{2011})}^{2011}}^{2010}$.

×