where 
is a monic polynomial of degree 
satisfying 
where 
and 
,
and 
if polynomial 
is a polynomial of degree 
such that 
Evaluate 
Prove that
and 
n
.
,
.
have roots 
.
.
(I won't be proving this here). This new information allows us to utilize the mean inequality chain as follows:
Similarly, applying AM-HM yields 
.
.
Y by
Let the polynomial 
have real roots and real coefficients with 
. What is the maximum value of 
?
This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):
Is this solution good?
have real roots and real coefficients with 
. What is the maximum value of 
?This is a problem I made for my math competition, and I wanted to see if someone would double-check my work (No Mike allowed):
Is this solution good?
This post has been edited 3 times. Last edited by BadAtCompetitionMath21420, May 17, 2025, 3:16 AM
Reason: No scrumptious allowed
Reason: No scrumptious allowed
(confirming that 
is actually possible)
imply 
?
and 
is a set of solutions that makes 
larger.
