Prove that
such that 
prove that![\[
a + b + c + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq 10.
\]](http://latex.artofproblemsolving.com/4/b/6/4b63bb9783dc4db8a6f91fcd083abfef92073480.png)
,
.
Y by HoripodoKrishno, Rounak_iitr, Mango247
Consider a polynomial ![$P(x) \in \mathbb{R}[x]$](//latex.artofproblemsolving.com/4/5/3/453a624c3b002c1b0e78e0023b24dd22ddd03557.png)
, with degree 
, such that 
for all 
. If the sum of all roots of 
is equal to 
with 
coprime, then what is the product 
?
![$P(x) \in \mathbb{R}[x]$](http://latex.artofproblemsolving.com/4/5/3/453a624c3b002c1b0e78e0023b24dd22ddd03557.png)
, with degree 
, such that 
for all 
. If the sum of all roots of 
is equal to 
with 
coprime, then what is the product 
?
is a root of 
then so is 
.
is odd, this forces one root of 
and the others can be paired up into roots summing to one. Thus sum of roots is 
and answer is 
.
(with 
)
in 
is 
and must be zero and so 
now note that 
is a zero poly.
so the roots of 
are also 
s
we see that coefficient of 
which basically gives us 
