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2
2024 Alg/NT Problem 2
2024 Alg/NT Problem 2
Source:
April 14, 2024
algebra
Problem Statement
Suppose
P
(
x
)
=
x
2
+
A
x
+
B
P(x)=x^2+Ax+B
P
(
x
)
=
x
2
+
A
x
+
B
for real
A
A
A
and
B
B
B
. If the sum of the roots of
P
(
2
x
)
P(2x)
P
(
2
x
)
is
1
2
\tfrac 12
2
1
and the product of the roots of
P
(
3
x
)
P(3x)
P
(
3
x
)
is
1
3
\tfrac 13
3
1
, find
A
+
B
A+B
A
+
B
.Proposed by Connor Gordon
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