Susan is traveling from queens to staten island via manhattan. there are 3 different trains that travel from her home in queens to times square, 5 trains that run from times square to the staten island ferry, and 2 buses that run from the staten island ferry to her home in staten island. how many different ways can susan get from queens to her home, passing through times square and the staten island ferry?

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.