If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 24 x + 16 = 0$.

While selling a pen for Rs. $24$, the loss percentage is equal to its cost price in rupees. Find the cost price of the pen.

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?

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.)

The value of discriminant $D$ for the equation $(3x - 14)^2 = 0$ is ........

The value of the discriminant of a quadratic equation $kx^{2} - 4x - 4 = 0$ is $64$,then $k = \dots$