Let α_θ and β_θ be the distinct roots of 2x² + (cos θ) x - 1 = 0, θ (0, 2π). If m and M are the minimum and the maximum values of α_θ⁴ + β_θ⁴, then 16(M + m) equals:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q42

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha_\theta

and

\beta_\theta

be the distinct roots of

2x^2 + (\cos \theta) 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: