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Finland Contests
Finnish National High School Mathematics Competition
2013 Finnish National High School Mathematics Competition
1
1
Part of
2013 Finnish National High School Mathematics Competition
Problems
(1)
Determine a monic cubic
Source: Finland 2013, Problem 1
5/2/2013
The coefficients
a
,
b
,
c
a,b,c
a
,
b
,
c
of a polynomial
f
:
R
ā
R
,
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
f:\mathbb{R}\to\mathbb{R}, f(x)=x^3+ax^2+bx+c
f
:
R
ā
R
,
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
are mutually distinct integers and different from zero. Furthermore,
f
(
a
)
=
a
3
f(a)=a^3
f
(
a
)
=
a
3
and
f
(
b
)
=
b
3
.
f(b)=b^3.
f
(
b
)
=
b
3
.
Determine
a
,
b
a,b
a
,
b
and
c
c
c
.
algebra
polynomial
quadratics
algebra unsolved