Examine whether the following equation is quadratic or not: $(3x + 1)(3x + 2) = (9x - 1)(x + 1)$

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 $k$?

$A$ two-digit number is such that the product of its digits is $6$. When $9$ is subtracted from the number,the resulting number is the number obtained by interchanging the digits. Find the original number.

The necessary condition for $ax^2 + bx + c = 0$,where $a, b, c \in R$,to be a quadratic equation is:

Represent the following situation in the form of a quadratic equation:
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.

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