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2021 German National Olympiad
1
1
Part of
2021 German National Olympiad
Problems
(1)
Roots of two quadratic equations
Source: Germany 2021, Problem 1
6/16/2021
Determine all real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
and
d
d
d
with the following property: The numbers
a
a
a
and
b
b
b
are distinct roots of
2
x
2
−
3
c
x
+
8
d
2x^2-3cx+8d
2
x
2
−
3
c
x
+
8
d
and the numbers
c
c
c
and
d
d
d
are distinct roots of
2
x
2
−
3
a
x
+
8
b
2x^2-3ax+8b
2
x
2
−
3
a
x
+
8
b
.
quadratics
algebra
algebra proposed
quadratic equation
roots