The price of corn oil is ₹ $x$ per $kg$. If the price of corn oil is decreased by ₹ $10$ per $kg$,then how many kilograms of corn oil can be obtained for ₹ $500$ at the new rate?

Obtain the roots of the following quadratic equation by using the quadratic formula: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

If one of the roots of quadratic equation $x^{2}+4x+m=0$ is $2$,then the other root is .... .

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

Represent the following situation mathematically:
John and Jivanti together have $45$ marbles. Both of them lost $5$ marbles each,and the product of the number of marbles they now have is $124$. We would like to find out how many marbles they had to start with.

Find the roots of the following quadratic equation,if they exist,by the method of completing the square: $4x^{2} + 4\sqrt{3}x + 3 = 0$.