Let \(\alpha_\theta\) and \(\beta_\theta\) be the distinct roots of \(2 \mathrm{x}^2+(\cos \theta) \mathrm{x}-1=0, \thet…

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

[JEE Main 2025, 22 Jan (Shift 2)]