If $a+b+c=0,$ then find the value of $a^{3}+b^{3}+c^{3}$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $12 x^{2} + 11 x - 56 = 0$
$II.$ $4 y^{2} - 15 y + 14 = 0$

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{x + 2}{x - 1} < 4$ is:

Both the roots of the given equation $(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0$ are always

If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$,then the other roots are

If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b = 0$ and if $\alpha^n + \beta^n = V_n$,then