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Regional Mathematical Olympiad
2018 India Regional Mathematical Olympiad
2
Polynomial in GP
Polynomial in GP
Source: RMO 2018 P2
October 28, 2018
algebra
polynomial
Problem Statement
Find the set of all real values of
a
a
a
for which the real polynomial equation
P
(
x
)
=
x
2
−
2
a
x
+
b
=
0
P(x)=x^2-2ax+b=0
P
(
x
)
=
x
2
−
2
a
x
+
b
=
0
has real roots, given that
P
(
0
)
⋅
P
(
1
)
⋅
P
(
2
)
≠
0
P(0)\cdot P(1)\cdot P(2)\neq 0
P
(
0
)
⋅
P
(
1
)
⋅
P
(
2
)
=
0
and
P
(
0
)
,
P
(
1
)
,
P
(
2
)
P(0),P(1),P(2)
P
(
0
)
,
P
(
1
)
,
P
(
2
)
form a geometric progression.
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