Solve the given two equations and select the correct answer from the given options.
$I. x - 7\sqrt{3x} + 36 = 0$
$II. y - 12\sqrt{2y} + 70 = 0$

If $\alpha, \beta$ are the roots of $x^2 - 3x + a = 0$ and $\gamma, \delta$ are the roots of $x^2 - 12x + b = 0$,and the numbers $\alpha, \beta, \gamma, \delta$ (in that order) form an increasing $G.P.$,then:

If one root of $ax^2 + bx + c = 0$ is the square of the other,then the value of $b^3 + ac^2 + a^2c$ is

Solve the given two equations and select the correct answer from the given options:
$I.$ $679 x^{2} - 168 x^{2} = 3066$
$II.$ $\sqrt{144} y^{3} - 9 y^{3} = 1536$

If $z_1, z_2, z_3, z_4$ are the roots of the equation $z^4 + z^3 + z^2 + z + 1 = 0$,then $\prod_{i=1}^{4} (z_i + 2)$ is equal to:

The coefficient of $x$ in the equation $x^2 + px + q = 0$ was taken as $17$ in place of $13$. Its roots were found to be $-2$ and $-15$. The roots of the original equation are: