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2008 PUMaC Team B8
Source:
October 4, 2019
algebra
Problem Statement
Suppose that the roots of the quadratic
x
2
+
a
x
+
b
x^2 + ax + b
x
2
+
a
x
+
b
are
α
\alpha
α
and
β
\beta
β
. Then
α
3
\alpha^3
α
3
and
β
3
\beta^3
β
3
are the roots of some quadratic
x
2
+
c
x
+
d
x^2 + cx + d
x
2
+
c
x
+
d
. Find
c
c
c
in terms of
a
a
a
and
b
b
b
.
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