A shelf is designed so it will fit in a 90º corner between two walls. The shelf has dimensions, rounded to the nearest tenth, as shown. A triangle has side lengths 11 centimeters, 11 centimeters, and hypotenuse of StartRoot 242 EndRoot centimeters. [Not drawn to scale] Will the shelf fit snugly in a 90º corner?

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.

the answer is  

c.

14,469 cubic feet

i know this one is right