If $p$ and $q$ are the roots of the equation ${x^2} + pq = (p + 1)x$,then $q=$

If $\alpha, \beta, \gamma$ are the roots of $x^3 - x - 2 = 0$,then the value of $\alpha^5 + \beta^5 + \gamma^5$ is-

$I. 3x^2 - 20x - 32 = 0$
$II. 2y^2 - 3y - 20 = 0$

If the inequality $kx^2 - 2x + k \geq 0$ holds good for at least one real $x$,then the complete set of values of $k$ is

Solve the given two equations and select the correct answer from the given options.
$I.$ $5x^{2} + 2x - 3 = 0$
$II.$ $2y^{2} + 7y + 6 = 0$

If $\alpha, \beta$ and $\gamma$ are three consecutive terms of a non-constant $G.P.$ such that the equations $\alpha x^2 + 2\beta x + \gamma = 0$ and $x^2 + x - 1 = 0$ have a common root,then $\alpha(\beta + \gamma)$ is equal to