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Problems
Contests
National and Regional Contests
Brazil Contests
Olympic Revenge
2020 Olympic Revenge
1
1
Part of
2020 Olympic Revenge
Problems
(1)
Non-zero coeficients
Source: Brazilian Olympic Revenge 2020, P1
2/1/2020
Let
n
n
n
be a positive integer and
a
1
,
a
2
,
…
,
a
n
a_1, a_2, \dots, a_n
a
1
,
a
2
,
…
,
a
n
non-zero real numbers. What is the least number of non-zero coefficients that the polynomial
P
(
x
)
=
(
x
−
a
1
)
(
x
−
a
2
)
⋯
(
x
−
a
n
)
P(x) = (x - a_1)(x - a_2)\cdots(x - a_n)
P
(
x
)
=
(
x
−
a
1
)
(
x
−
a
2
)
⋯
(
x
−
a
n
)
can have?
olympic revenge
Brazil
algebra