Solve the given two equations and select the correct option.
$I.$ $63x^2 + 172x + 117 = 0$
$II.$ $30y^2 + 162y + 216 = 0$

If $p$ and $q$ are non-zero real numbers and $\alpha^3 + \beta^3 = -p$,$\alpha \beta = q$,then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}$ and $\frac{\beta^2}{\alpha}$ is

Let $\alpha$ and $\beta$ be two roots of the equation $x^2 + 2x + 2 = 0$. Then,$\alpha^{15} + \beta^{15}$ is equal to:

Solve the given two equations and select the correct answer from the given options.
$I.$ $2.3x - 20.01 = 0$
$II.$ $2.9y - x = 0$

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$,find the value of $\alpha^{2}+\beta^{2}$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{15}{\sqrt{x}}-\frac{9}{\sqrt{x}}=(x)^{\frac{1}{2}}$
$II.$ $y^{10}-(36)^{5}=0$