MathDB
Problems
Contests
International Contests
Austrian-Polish
1996 Austrian-Polish Competition
3
3
Part of
1996 Austrian-Polish Competition
Problems
(1)
Polynomial and equation
Source: Austrain Polish 1996
12/7/2013
The polynomials
P
n
(
x
)
P_{n}(x)
P
n
(
x
)
are defined by
P
0
(
x
)
=
0
,
P
1
(
x
)
=
x
P_{0}(x)=0,P_{1}(x)=x
P
0
(
x
)
=
0
,
P
1
(
x
)
=
x
and P_{n}(x)=xP_{n-1}(x)+(1-x)P_{n-2}(x) n\geq 2 For every natural number
n
≥
1
n\geq 1
n
≥
1
, find all real numbers
x
x
x
satisfying the equation
P
n
(
x
)
=
0
P_{n}(x)=0
P
n
(
x
)
=
0
.
algebra
polynomial
recurrence relation