The equation x⁴ - 2x³ − 1 = 0 has roots α, β, γ, δ.

The cubic equation x³ – px − q = 0, where p and q are constants, has roots α, β, γ. Show that

Answer only one of the following two alternatives. EITHER The roots of the quartic equation x⁴ + 4x³ + 2x² – 4x + 1 =…

The cubic equation x³ + px² + qx + r = 0, where p, q and r are integers, has roots α, β and γ, such that α + β + γ = …

The square matrix A has λ as an eigenvalue with e as a corresponding eigenvector. Show that e is an eigenvector of A²…

The plane Π₁ has equation r = [[2], [3], [-2]] + s[[1], [0], [-1]] + t[[0], [-1], [-2]]. Find a cartesian equation of…

The curve C has parametric equations x = t², y=t-t³, for 0 ≤ t ≤ 1. Find the surface area generated when C is rotated…