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2
Math Prize 2023 Problem 2
Math Prize 2023 Problem 2
Source:
October 11, 2023
Problem Statement
In the
x
y
xy
x
y
-coordinate plane, the horizontal line
y
=
k
y = k
y
=
k
intersects the graph of the cubic
2
x
3
+
6
x
2
ā
4
x
+
5
2x^3 + 6x^2 - 4x + 5
2
x
3
+
6
x
2
ā
4
x
+
5
in three points
P
P
P
,
Q
Q
Q
, and
R
R
R
. Given that
Q
Q
Q
is the midpoint of
P
P
P
and
R
R
R
, what is
k
k
k
?
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