# Too Many Greek Letters

Algebra Level 3

The polynomial $F(x)=x^6-2x^5+3x^{4}-4x^{3}+5x^{2}-6x+7$ has $6$ roots, namely $\alpha, \beta, \gamma, \theta, \sigma$ and $\omega$. The value of $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}+\frac{1}{\theta}+\frac{1}{\sigma}+\frac{1}{\omega}$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are coprime integers.

What is the value of $a \times b$?

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