Cody summer sells tires for tractor trailers. he earns 4.5% commission on the first $6,000 in sales, 8% commission on the next $6,000, and 12% commission on sales over $12,000. last month he sold $18,000 worth of tires. what was his total commission?
a) $1,540
b) $1,470
c) $1,450
d) $1,650

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.