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National and Regional Contests
Poland Contests
Poland - Second Round
1951 Poland - Second Round
4
4
Part of
1951 Poland - Second Round
Problems
(1)
(n - q)^2 - (m - p) (np - mq) = 0
Source: Polish MO second round 1951 p4
8/28/2024
Prove that if equations
x
2
+
m
x
+
n
=
0
a
n
d
x
2
+
p
x
+
q
=
0
x^2 + mx + n = 0 \,\,\,\, and\,\, \,\, x^2 + px + q = 0
x
2
+
m
x
+
n
=
0
an
d
x
2
+
p
x
+
q
=
0
have a common root, there is a relationship between the coefficients of these equations
(
n
−
q
)
2
−
(
m
−
p
)
(
n
p
−
m
q
)
=
0.
(n - q)^2 - (m - p) (np - mq) = 0.
(
n
−
q
)
2
−
(
m
−
p
)
(
n
p
−
m
q
)
=
0.
algebra
trinomial