Polynomials

The zeroes of p(x) = x² + 2x - 15 are:

If α, β, γ are zeroes of x³ - 3x² + x + 1, then (1/α) + (1/β) + (1/γ) equals:

If \(\alpha, \beta\) are zeroes of \(x^{2} - 1\), find the value of \(\alpha^{2} - \beta^{2}\).

If \(\alpha, \beta\) are zeroes of \(x^{2} - kx + 12\), and \(\alpha - \beta = 1\), find \(k\).

If \(\alpha, \beta\) are zeroes of \(p(x) = x^{2} - 5x + 6\), find the value of \(\alpha^{3} + \beta^{3} + 3\alpha\beta\).