By finding a cubic equation whose roots are α, β and γ, solve the set of simultaneous equations α + β + γ = −1, α² + β² + γ² = 29, 1/α + 1/β + 1/γ = −1.

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 = …

A curve C is defined parametrically by x = 2/(eᵗ + e⁻ᵗ) and y = (eᵗ - e⁻ᵗ)/(eᵗ + e⁻ᵗ), for 0 ≤ t ≤ 1. The area of the…

Find the particular solution of the differential equation 10d²x/dt² + 3dx/dt - x = t + 2, given that when t = 0, x = …

Prove by mathematical induction that, for z ≠ 1 and all positive integers n, 1 + z + z² + ... + zⁿ⁻¹ = (zⁿ - 1)/(z - 1)