Let Pₙ = αⁿ + βⁿ, n ∈ ℕ. If P₁₀ = 123, P₉ = 76, P₈ = 47 and P₁ =… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 2 April, Shift 1Sum of Series

Let $P_n = \alpha^n + \beta^n$ , $n \in \mathbb{N}$ . If $P_{10} = 123,\ P_9 = 76,\ P_8 = 47$ and $P_1 = 1$ , then the quadratic equation having roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is:

A
$x^2 - x + 1 = 0$
B
$x^2 + x - 1 = 0$
C
$x^2 - x - 1 = 0$
D
$x^2 + x + 1 = 0$

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