Too Many Greek Letters

Algebra Level 3

The polynomial F(x)=x62x5+3x44x3+5x26x+7F(x)=x^6-2x^5+3x^{4}-4x^{3}+5x^{2}-6x+7 has 66 roots, namely α,β,γ,θ,σ\alpha, \beta, \gamma, \theta, \sigma and ω\omega. The value of 1α+1β+1γ+1θ+1σ+1ω\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}+\frac{1}{\theta}+\frac{1}{\sigma}+\frac{1}{\omega} can be expressed as ab\frac{a}{b}, where aa and bb are coprime integers.

What is the value of a×ba \times b?

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