Find the roots of the following quadratic equation by factorisation:
$100 x^{2}-20 x+1=0$

Check whether the following is a quadratic equation:
$x^{2}-2x=(-2)(3-x)$

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.

Check whether the following is a quadratic equation:
$(2x - 1)(x - 3) = (x + 5)(x - 1)$

Two water taps together can fill a tank in $9 \frac{3}{8}$ hours. The tap of larger diameter takes $10 \text{ hours}$ less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Check whether the following is a quadratic equation:
$x(x+1)+8=(x+2)(x-2)$