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2021 MOAA
15
Team Round P15
Team Round P15
Source:
October 16, 2021
MOAA 2021
team
Problem Statement
Consider the polynomial
P
(
x
)
=
x
3
+
3
x
2
+
6
x
+
10.
P(x)=x^3+3x^2+6x+10.
P
(
x
)
=
x
3
+
3
x
2
+
6
x
+
10.
Let its three roots be
a
a
a
,
b
b
b
,
c
c
c
. Define
Q
(
x
)
Q(x)
Q
(
x
)
to be the monic cubic polynomial with roots
a
b
ab
ab
,
b
c
bc
b
c
,
c
a
ca
c
a
. Compute
∣
Q
(
1
)
∣
|Q(1)|
∣
Q
(
1
)
∣
.Proposed by Nathan Xiong
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