Under which one of the following conditions does the equation (cosβ - 1)x² + (cosβ)x + sinβ = 0 have a real root for β ∈ [0, π]? - NDA Mathematics 2024 (I)

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Under which one of the following conditions does the equation (cosβ – 1)x² + (cosβ)x + sinβ = 0 have a real root for β ∈ [0, π]?