The value of discriminant $D$ of the quadratic equation $25x^{2} - 10x + 1 = 0$ is ..... .

Obtain the roots of the following equation using the method of 'completing the square': $16x^{2} - 24x - 1 = 0$.

If the roots of the quadratic equation $x(x+1)-6=0$ are

Obtain the roots of the following equation using the method of 'completing the square': $6x^2 + 11x + 3 = 0$

Divide $16$ into two parts such that twice the square of the larger part exceeds the square of the smaller part by $164$.

The formula to find the sum $S$ of the first $n$ natural numbers is $S = \frac{n(n+1)}{2}$. Find $n$ if the sum of the first $n$ natural numbers is $300$.