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

$Quantity \, 1:$ Original duration of flight. In a flight of $3000 \, km$,an aircraft was slowed down by bad weather. Its average speed for the trip was reduced by $100 \, km/hr$ and the time increased by $1 \, hour$.
$Quantity \, 2:$ Usual time of a man who,when walking at $\frac{3}{4}$ of his usual pace,reaches his office $20 \, minutes$ late.

The value of $k$ for which the equation $(k - 2)x^2 + 8x + (k + 4) = 0$ has both roots real,distinct,and negative is

$P$ can complete a piece of work in $16$ days,which $Q$ can complete in $32$ days. If $P$ and $Q$ work on alternate days,find the relationship between Quantity $I$ (Total days taken if $P$ starts) and Quantity $II$ (Total days taken if $Q$ starts).

If $\left(\frac{p^{-1} q^{2}}{p^{3} q^{-2}}\right)^{\frac{1}{3}}+\left(\frac{p^{5} q^{-3}}{p^{-2} q^{3}}\right)^{\frac{1}{3}}=p^{a} q^{b},$ then the value of $a+b,$ where $p$ and $q$ are different positive positive primes,is

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then