The roots of the equation $x^2 + ax + b = 0$ are $p$ and $q$. Then,the equation whose roots are $p^2q$ and $pq^2$ will be:

Let $\alpha$ and $\beta$ be the roots of the equation $x^{2}-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?

The number of integral values of $m$ for which the equation $(1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0$ has no real root is

Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then the integral values of $p, q$ are respectively:

$Quantity$ $1$: Height of the tank if the volume of a cylindrical tank is $12320 \, cm^3$. Its radius and height are in the ratio of $7:10$ respectively. $Quantity$ $2$: Height of the kerosene level in a jar if a cone of radius $2 \, cm$ and height $3 \, cm$ is melted and recast into a cylinder of radius $2 \, cm$.

If $8, 2$ are the roots of ${x^2} + ax + \beta = 0$ and $3, 3$ are the roots of ${x^2} + \alpha x + b = 0$,then the roots of ${x^2} + ax + b = 0$ are