The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

The speed of a motorboat in still water is $25 \text{ km/hr}$. In a river, it covers $60 \text{ km}$ downstream and the same distance upstream in a total time of $5 \text{ hours}$. Find the speed of the current of the river. (The speed of the current of the river is less than the speed of the motorboat in still water.) (in $\text{ km/hr}$)

When there is a decrease of $5\, km/hr$ in the usual uniform speed of a train,it takes $4$ hours more than the usual time for covering the distance of $400\, km$. Find the usual speed of the train.

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

Find the roots of the following quadratic equation using the quadratic formula,if they exist: $\frac{1}{x+1} + \frac{2}{x+2} = \frac{4}{x+4}$; $(x \neq -1, -2, -4)$

Find the roots of the following quadratic equation by the method of completing the square: $x^{2}-4 \sqrt{2} x+6=0$