If the following quadratic equation has two equal and real roots,then find the value of $k$: $x(4 - kx) = 3 - 2x$.

Write whether the following statements are true or false. Justify your answers.
$(i)$ If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of $x$ term is zero,then the quadratic equation has no real roots.
$(ii)$ Every quadratic equation has at least two roots.

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 $300$.

We get $2 \ kg$ of pure butter less in Rs. $960$ if the price of pure butter increases by Rs. $40$ per $kg$. Find the original price of pure butter per kilogram.

Examine whether the following equation is quadratic or not: $x^{2}+\frac{1}{x^{2}}=-2$ $(x \neq 0)$

The roots of a quadratic equation $x^{2} = 49$ are ..... .