If the roots of the equation $lx^2 + nx + n = 0$ are in the ratio $p:q$,then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} + \sqrt{\frac{n}{l}} = $

If $x^2-3x+2$ is a factor of $x^4-ax^2+b$,then the equation whose roots are $a$ and $b$ is

The condition to be satisfied in order that one root of $x^3+b x^2+c x+d=0$ is the sum of the other two roots,is

Let $\alpha$ and $\beta$ be the roots of the equation $px^2+qx-r=0$,where $p \neq 0$. If $p, q,$ and $r$ are the consecutive terms of a non-constant $G$.$P$. and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$,then the value of $(\alpha-\beta)^2$ is:

If $\lambda \in R$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2 - \lambda)x + (10 - \lambda) = 0$ is minimum,then the magnitude of the difference of the roots of this equation is

If $\alpha, \beta$ are the roots of the equation $x^2 - px + r = 0$ and $\alpha/2, 2\beta$ are the roots of the equation $x^2 - qx + r = 0$,then what is the value of $r$?