Why is it important to have categories of numbers in to know which category you're doing with the given expression

A way to categorize information and point you to where to find that information is called the table of contents. It contains the chapters of the topic and its corresponding subtopic. It depends on the length of the topic of that book or section. It is located at the first few pages of the book or other reading material.  

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.