A freight train left Berlin and traveled west at an average speed of 90 mph. A
passenger train left six hours later and
traveled in the opposite direction with an
average speed of 40 mph. Find the
number of hours the passenger train needs
to travel before the trains are 930 mi.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.

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.