The cubic equation x³ – 2x² – 3x + 4 = 0 has roots α, β, γ. Given that c = α + β + γ, state the value of c. Use the substitution y = c − x to find a cubic equation whose roots are α + β, β + γ, γ + α. Find a cubic equation whose roots are 1/(α + β), 1/(β + γ), 1/(γ + α). Hence evaluate 1/(α + β)² + 1/(β + γ)² + 1/(γ + α)².

The roots of the cubic equation x³ – 7x² + 2x – 3 = 0 are α, β, γ. Find the values of

The equation x³ + px + q = 0, where p and q are constants, with q ≠ 0, has one root which is the reciprocal of anothe...

The roots of the cubic equation x³ – 7x² + 2x − 3 = 0 are α, β and γ. Find the values of Deduce a cubic equation, wit...

The sum S_N is defined by S_N = ∑_{n=1}^N n³. Using the identity (n+1)⁶ – (n-1)⁶ = 6n⁵ + 5n³ + 3n, find S_N in terms ...

Let I_n = ∫_1^e x(lnx)ⁿ dx, where n ≥ 1.

The lines l₁ and l₂ have vector equations r = 4i – 2j + λ(2i + j – 4k) and r = 4i – 5j + 2k + μ(i – j – k) respectively.