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.)

Which of the following is a quadratic equation?

Which constant must be added and subtracted to solve the quadratic equation $9x^{2} + \frac{3}{4}x - \sqrt{2} = 0$ by the method of completing the square?

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $\frac{1}{4} x^{2} - 2x + 1 = 0$.

The speed of a motorboat in still water is $9\,km/h$. In a river,it covers $12\,km$ downstream and the same distance upstream in a total time of $3\,hours$. Find the speed of the current of the river. (The speed of the current of the river is less than the speed of the motorboat in still water.) (in $,km/h$)

The length of a rectangle is $2\,cm$ less than $3$ times its breadth. If its area is $280\,cm^2$,then find its length.