If $3$ is a root of the quadratic equation $x^{2}-kx+6=0$,then $k = \ldots$

$A$ prayer hall has a carpet area of $300 \ m^2$ with its length one metre more than twice its breadth. Find the dimensions of the prayer hall.

Examine whether the following equation is quadratic or not: $(3x - 4)^2 - (2x - 3)^2 = 7$.

Represent the following situation in the form of a quadratic equation:
$A$ train travels a distance of $480 \, km$ at a uniform speed. If the speed had been $8 \, km/h$ less,then it would have taken $3 \, hours$ more to cover the same distance. We need to find the speed of the train.

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

Solve the following equation using the method of 'completing the square': $4 x^{2}+3 x+5=0$