Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 9 feet and a height of 12 feet. Container B has a radius of 7 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Containter B is completely full. After the pumping is complete, what is the volume of water remaining in Container A, to the nearest tenth of a cubic foot?

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.

answer: the answer is 110