MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia MO
2021 Indonesia MO
5
5
Part of
2021 Indonesia MO
Problems
(1)
simple polynomial -- prove an inequality
Source: Indonesia National Math Olympiad 2021 Problem 5 (INAMO 2021/5)
11/9/2021
Let
P
(
x
)
=
x
2
+
r
x
+
s
P(x) = x^2 + rx + s
P
(
x
)
=
x
2
+
r
x
+
s
be a polynomial with real coefficients. Suppose
P
(
x
)
P(x)
P
(
x
)
has two distinct real roots, both of which are less than
ā
1
-1
ā
1
and the difference between the two is less than
2
2
2
. Prove that
P
(
P
(
x
)
)
>
0
P(P(x)) > 0
P
(
P
(
x
))
>
0
for all real
x
x
x
.
algebra
polynomial
inequalities