If both the roots of a quadratic equation $kx^{2} + 4x + 1 = 0$ are equal,then $k = \ldots$

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 $300$.

Examine whether the following equation is quadratic or not: $(x-2)^{2}+1=2x-3$.

Solve the following equation using the method of factorization and write its solution set: $\frac{9}{x-1} - \frac{2}{x-3} = \frac{5}{x+1}$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $6x^{2}-x-2=0, x=3$.

The roots of the quadratic equation $x^{2}+18x+81=0$ are ..... .