Let α be a solution of x² + x + 1 = 0, and for some a and b in R, [4 a b] 1 16 13 -1 -1 2 -2 -14 -8 = [0 0 0]. If 4/(α⁴) + m/(α) + n/(α²) = 3, then m + n is equal to

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q202

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

Let

\alpha

be a solution of

x^2 + x + 1 = 0

, and for some a and b in

\mathbb{R}

[4 \; a \; b] \begin{bmatrix}1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8\end{bmatrix} = [0 \; 0 \; 0]

. If

\frac{4}{\alpha^4} + \frac{m}{\alpha} + \frac{n}{\alpha^2} = 3

, then m + n is equal to