Answer only one of the following two alternatives. EITHER The roots of the quartic equation x⁴ + 4x³ + 2x² – 4x + 1 = 0 are α, β, γ and δ. Find the values of (i) α + β + γ + δ, (ii) α² + β² + γ² + δ², (iii) 1/α + 1/β + 1/γ + 1/δ, (iv) α/(βγδ) + β/(αγδ) + γ/(αβδ) + δ/(αβγ). Using the substitution y = x + 1, find a quartic equation in y. Solve this quartic equation and hence find the roots of the equation x⁴ + 4x³ + 2x² − 4x + 1 = 0. OR The square matrix A has λ as an eigenvalue with e as a corresponding eigenvector. Show that if A is non-singular then (i) λ ≠ 0, (ii) the matrix A⁻¹ has λ⁻¹ as an eigenvalue with e as a corresponding eigenvector. The 3 × 3 matrices A and B are given by A = ((-2, 2, -4), (0, -1, 5), (0, 0, 3)) and B = (A + 3I)⁻¹, where I is the 3 × 3 identity matrix. Find a non-singular matrix P, and a diagonal matrix D, such that B = PDP⁻¹.