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India LIMIT
2020 LIMIT
2020 LIMIT Category 1
7
Exploiting Vieta's relations
Exploiting Vieta's relations
Source: LIMIT 2020 Cat 1 Obj P7
May 2, 2020
algebra
polynomial
limit
Vieta
Problem Statement
Let
P
(
x
)
=
x
6
−
x
5
−
x
3
−
x
2
−
x
P(x)=x^6-x^5-x^3-x^2-x
P
(
x
)
=
x
6
−
x
5
−
x
3
−
x
2
−
x
and
a
,
b
,
c
a,b,c
a
,
b
,
c
and
d
d
d
be the roots of the equation
x
4
−
x
3
−
x
2
−
1
=
0
x^4-x^3-x^2-1=0
x
4
−
x
3
−
x
2
−
1
=
0
, then determine the value of
P
(
a
)
+
P
(
b
)
+
P
(
c
)
+
P
(
d
)
P(a)+P(b)+P(c)+P(d)
P
(
a
)
+
P
(
b
)
+
P
(
c
)
+
P
(
d
)
(A)
5
5
5
(B)
6
6
6
(C)
7
7
7
(D)
8
8
8
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