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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1976 Dutch Mathematical Olympiad
4
4
Part of
1976 Dutch Mathematical Olympiad
Problems
(1)
x^2 - (2a^2 + 4)x + a^2 + 2a + b = 0
Source: Netherlands - Dutch NMO 1976 p4
1/28/2023
For
a
,
b
,
x
∈
R
a,b, x \in R
a
,
b
,
x
∈
R
holds:
x
2
−
(
2
a
2
+
4
)
x
+
a
2
+
2
a
+
b
=
0
x^2 - (2a^2 + 4)x + a^2 + 2a + b = 0
x
2
−
(
2
a
2
+
4
)
x
+
a
2
+
2
a
+
b
=
0
. For which
b
b
b
does this equation have at least one root between
0
0
0
and
1
1
1
for all
a
a
a
?
algebra
parameter
parameterization
equation
trinomial