Show that #f# has at least one root in #RR# ?
Given #f:RR>RR# , continuous with #f(a)+f(b)+f(c)=0# , #a,b,c# #in# #RR#
Given
2 Answers
Check below.
Explanation:
Got it now.
For
We can either have

#f(a)=0# and#f(b)=0# and#f(c)=0# which means that#f# has at least one root,#a# ,#b# ,#c# 
One of the two numbers at least to be opposite between them
Let's suppose
That means
According to Bolzano's theorem there is at least one
Using Bolzano's theorem in other intervals
Eventually
See below.
Explanation:
If one of
Now supposing
will be true, otherwise
will imply that
In each case the result for
Now if one of