Let α_θ and β_θ be the distinct roots of 2 x^2+( cos θ) x-1=0, θ ∈(0,2 π). If m and M are the minimum and the maximum values of α_θ^4+β_θ^4, then 16(…

Let $\displaystyle \alpha_\theta$ and $\displaystyle \beta_\theta$ be the distinct roots of $\displaystyle 2 x^2+(\cos \theta) x-1=0, \theta \in(0,2 \pi)$. If m and M are the minimum and the maximum values of $\displaystyle \alpha_\theta^4+\beta_\theta^4$, then $\displaystyle 16(\mathrm{M}+\mathrm{m})$ equals :