MathDB
Problems
Contests
National and Regional Contests
Kosovo Contests
Kosovo National Mathematical Olympiad
2010 Kosovo National Mathematical Olympiad
3
Kosovo MO 2010 Grade 12, Problem 3
Kosovo MO 2010 Grade 12, Problem 3
Source: Kosovo MO 2010 Grade 12, Problem 3
June 7, 2021
algebra
Problem Statement
Let
n
∈
N
n\in \mathbb{N}
n
∈
N
. Prove that the polynom
p
(
x
)
=
x
2
n
−
2
x
2
n
−
1
+
3
x
2
n
−
2
−
.
.
.
−
2
n
x
+
2
n
+
1
p(x)=x^{2n}-2x^{2n-1}+3x^{2n-2}-...-2nx+2n+1
p
(
x
)
=
x
2
n
−
2
x
2
n
−
1
+
3
x
2
n
−
2
−
...
−
2
n
x
+
2
n
+
1
doesn't have real roots.
Back to Problems
View on AoPS