Which of the following expressions are meaningful? which are meaningless? explain. (a) (a · b) · c (a · b) · c has because it is the dot product of . (b) (a · b)c (a · b)c has because it is a scalar multiple of . (c) |a|(b · c) |a|(b · c) has because it is the product of . (d) a · (b + c) a · (b + c) has because it is the dot product of . (e) a · b + c a · b + c has because it is the sum of . (f) |a| · (b + c) |a| · (b + c) has because it is the dot product of .

w'x is 0.

hope it

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 is 12345678900987654321234567890987654321

step-by-step explanation: