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Poland Contests
Poland - Second Round
1962 Poland - Second Round
2
2
Part of
1962 Poland - Second Round
Problems
(1)
ax^2 + 2bxy + cy^2 + 2dx + 2ey + f = P(x) Q(x)
Source: Polish MO Second Round 1962 p2
8/31/2024
What conditions should real numbers
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
,
e
e
e
,
f
f
f
meet in order for a polynomial of second degree
a
x
2
+
2
b
x
y
+
c
y
2
+
2
d
x
+
2
e
y
+
f
ax^2 + 2bxy + cy^2 + 2dx + 2ey + f
a
x
2
+
2
b
x
y
+
c
y
2
+
2
d
x
+
2
ey
+
f
was the product of two first degree polynomials with real coefficients ?
algebra
polynomial