Examine whether the following equation is quadratic or not: $(x+6)(x+5)=0$.

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 $\text{ km/hr}$)

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

The sum of two natural numbers is $5$ and the sum of their reciprocals is $\frac{5}{6}$. Find those numbers.

State whether the quadratic equation $(x+1)(x-2)+x=0$ has two distinct real roots. Justify your answer.

The standard form of a quadratic polynomial of one variable is $\ldots .$