If $\alpha , \beta , \gamma$ are roots of equation $x^3 + qx -r = 0$ then the equation, whose roots are

$\left( {\beta \gamma  + \frac{1}{\alpha }} \right),\,\left( {\gamma \alpha  + \frac{1}{\beta }} \right),\,\left( {\alpha \beta  + \frac{1}{\gamma }} \right)$

If $(x + 1)$ is a factor of ${x^4} – (p – 3){x^3} – (3p – 5){x^2}$ $ + (2p – 7)x + 6$, then $p = $

The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:

The two roots of an equation ${x^3} – 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be

If $x$ is a solution of the equation, $\sqrt {2x + 1}  – \sqrt {2x – 1}  = 1, \left( {x \ge \frac{1}{2}} \right)$ , then $\sqrt {4{x^2} – 1} $ is equal to