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Dutch BxMO/EGMO TST
2012 Dutch BxMO/EGMO TST
1
1
Part of
2012 Dutch BxMO/EGMO TST
Problems
(1)
P(Q(x)) has only the zeros at x= 2,3,5,7 wher P,Q trinomials
Source: Dutch BxMO/EGMO TST 2012 p1
8/24/2019
Do there exist quadratic polynomials
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
with real coeffcients such that the polynomial
P
(
Q
(
x
)
)
P(Q(x))
P
(
Q
(
x
))
has precisely the zeros
x
=
2
,
x
=
3
,
x
=
5
x = 2, x = 3, x =5
x
=
2
,
x
=
3
,
x
=
5
and
x
=
7
x = 7
x
=
7
?
trinomial
quadratics
polynomial
roots
algebra