|(x+1 x x) , (x x+λ x), (x x x+λ^2)| = 9/8 (103x + 81), then λ and λ/3 are roots

Question

\(\begin{vmatrix} x+1 & x & x \\ x & x+λ & x \\ x & x & x+λ^2 \end{vmatrix}\) = 9/8 (103x + 81), then λ and λ/3 are roots of 

(1) 4x² + 24x – 27 = 0 

(2) 4x² – 24x + 27 = 0 

(3) 4x² – 24x – 27 = 0 

(4) 4x² + 24x + 27 = 0

Answer 1

(2) 4x² – 24x + 27 = 0 

Put x = 0 in the given equation