If $x=2$ is one of the solutions of the quadratic equation $k x^{2}+3 x-4=0,$ then what is the value of $k$?

In Hindu civilization,$\ldots \ldots \ldots$ gave the method to solve quadratic equations.

$A$ train travels at a certain average speed for a distance of $63 \, km$ and then travels a distance of $72 \, km$ at an average speed of $6 \, km/h$ more than its original speed. If it takes $3 \, hours$ to complete the total journey,what is its original average speed in $km/h$?

The product of the digits of a two-digit number is $14$. The number obtained by interchanging the digits is $45$ more than the original number. Find the original number.

The roots of a quadratic equation $(x+2)^{2}=16$ are ..... .

Solve by using the quadratic formula. The area of a rectangular plot is $528 \ m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.