MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2014 Harvard-MIT Mathematics Tournament
4
2014 HMMT #4: Polynomial
2014 HMMT #4: Polynomial
Source:
February 23, 2014
HMMT
algebra
polynomial
Vieta
sum of roots
Problem Statement
Let
b
b
b
and
c
c
c
be real numbers and define the polynomial
P
(
x
)
=
x
2
+
b
x
+
c
P(x)=x^2+bx+c
P
(
x
)
=
x
2
+
b
x
+
c
. Suppose that
P
(
P
(
1
)
)
=
P
(
P
(
2
)
)
=
0
P(P(1))=P(P(2))=0
P
(
P
(
1
))
=
P
(
P
(
2
))
=
0
, and that
P
(
1
)
≠
P
(
2
)
P(1) \neq P(2)
P
(
1
)
=
P
(
2
)
. Find
P
(
0
)
P(0)
P
(
0
)
.
Back to Problems
View on AoPS