On a voyage to atlantis, ariel from the little mermaid decided to pick up shells so that she could make necklaces for her mermaid friends. she picked up 30 green shells, 35 blue shells, and 30 yellow shells. 17 of the green shells had some blue in them. 15 of the shells had both yellow and blue in them, and 10 of the shells had both yellow and green in them. if just one shell had all three colors in it, how many total shells did ariel pick up?

step-by-step explanation:

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.