The roots of the equation $x^{2}+px+q=0$ are equal if:

If the roots of the equation $ax^2 + bx + c = 0$ are $(\alpha - \beta)$ and $(\gamma - \delta)$,and the roots of the equation $Ax^2 + Bx + C = 0$ are $(\alpha + \delta)$ and $(\beta + \gamma)$,then $\left| \frac{a}{A} \right|$ is equal to (where $D_1$ and $D_2$ are the discriminants of the given equations respectively).

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

Solve the given two equations and select the correct option.
$I.$ $\sqrt{500} x + \sqrt{402} = 0$
$II.$ $\sqrt{360} y + \sqrt{200} = 0$

If $(1 - p)$ is a root of the quadratic equation $x^2 + px + (1 - p) = 0$,then its roots are:

If one root of the equation $x^2 + px + q = 0$ is the square of the other,then