Amir is sorting his stamp collection. he made a chart of the fraction of stamps from each country in his collection. \dfrac{7}{12} 12 7 start fraction, 7, divided by, 12, end fraction of amir's stamps are from either morocco or spain. country fraction of stamps france \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction spain ? ? question mark morocco \dfrac16 6 1 start fraction, 1, divided by, 6, end fraction slovenia \dfrac{1}{12} 12 1 start fraction, 1, divided by, 12, end fraction what fraction of amir's stamps are from spain? of amir's stamps

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.