If the following quadratic equation has two equal and real roots,then find the value of $k$: $3x^{2} - 18x + k = 0$.

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

When there is a decrease of $5\, km/hr$ in the usual uniform speed of a train,it takes $4$ hours more than the usual time for covering the distance of $400\, km$. Find the usual speed of the train.

If $3$ is a root of the quadratic equation $x^{2}-kx+6=0$,then $k = \ldots$

The discriminant of the equation $3x^2 - 6x + 4 = 0$ is .............

The quadratic equation having roots $-1$ and $2$ is .... .