Joel is going to start a business. To cover his start-up costs he takes out two loans. Loan 1: Joel made an initial payment of $2,000 and will make monthly payments of $300 per month. Loan 2: Joel made an initial payment of $1,000 and will make monthly payments of $200 per month. How many months will it take Joel to pay off these two loans if they are $21,500 in total?

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.