A pipe is at least 21 feet long and you want to cut it into three pieces. The second piece is to be twice as long as the third piece, and the third piece is to be 1 foot longer than the second piece. What is the mat A pipe is at least 21 feet long and you want to cut it into three pieces. The second piece is to be twice as long as the third piece, and the third piece is to be 1 foot longer than the second piece. What is the minimum length of the first piece?

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 ann

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative