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Let be roots of the eqn
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be roots of the eqn.
x
4
+
x
3
+
x
2
+
x
+
1
=
0
x^4 + x^3 + x^2 + x + 1 = 0
x
4
+
x
3
+
x
2
+
x
+
1
=
0
. Let
f
(
x
)
=
x
6
−
6
x
2
+
6
x
+
7
f(x) = x^6 - 6x^2 + 6x + 7
f
(
x
)
=
x
6
−
6
x
2
+
6
x
+
7
and
g
(
x
)
=
p
x
2
+
q
x
+
r
g(x) = px^2 + qx + r
g
(
x
)
=
p
x
2
+
q
x
+
r
(
p
,
q
,
r
∈
R
,
p
≠
0
p, q, r \in \mathbb{R}, p \neq 0
p
,
q
,
r
∈
R
,
p
=
0
). If
f
(
a
)
=
g
(
a
)
,
f
(
b
)
=
g
(
b
)
f(a) = g(a), f(b) = g(b)
f
(
a
)
=
g
(
a
)
,
f
(
b
)
=
g
(
b
)
&
f
(
c
)
=
g
(
c
)
f(c) = g(c)
f
(
c
)
=
g
(
c
)
, then the value of
g
(
1
)
g(1)
g
(
1
)
is - -
Related theory
Polynomials
Division Algorithm for Polynomials
Polynomial Functions
Functions
Binomial theorem
Algebra
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