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India IOQM
2023-24 IOQM India
12
IOQM 2023-24 P-12
IOQM 2023-24 P-12
Source:
September 3, 2023
algebra
polynomial
Problem Statement
Let
P
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
P(x)=x^3+ax^2+bx+c
P
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
be a polynomial where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers and
c
c
c
is odd. Let
p
i
p_{i}
p
i
be the value of
P
(
x
)
P(x)
P
(
x
)
at
x
=
i
x=i
x
=
i
. Given that
p
1
3
+
p
2
3
+
p
3
3
=
3
p
1
p
2
p
3
p_{1}^3+p_{2}^{3}+p_{3}^{3}=3p_{1}p_{2}p_{3}
p
1
3
+
p
2
3
+
p
3
3
=
3
p
1
p
2
p
3
, find the value of
p
2
+
2
p
1
−
3
p
0
.
p_{2}+2p_{1}-3p_{0}.
p
2
+
2
p
1
−
3
p
0
.
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