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Let be real numbers
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Let
a
,
b
,
c
,
d
,
e
,
f
a, b, c, d, e, f
a
,
b
,
c
,
d
,
e
,
f
be real numbers. Define the polynomials
P
(
x
)
=
2
x
4
−
26
x
3
+
a
x
2
+
b
x
+
c
P(x) = 2x^4 - 26x^3 + ax^2 + bx + c
P
(
x
)
=
2
x
4
−
26
x
3
+
a
x
2
+
b
x
+
c
and
Q
(
x
)
=
5
x
4
−
80
x
3
+
d
x
2
+
e
x
+
f
Q(x) = 5x^4 - 80x^3 + dx^2 + ex + f
Q
(
x
)
=
5
x
4
−
80
x
3
+
d
x
2
+
e
x
+
f
. Let
S
S
S
be the set of all those numbers which are a root of either
P
P
P
or
Q
Q
Q
(or both). Given that
S
=
{
1
,
2
,
3
,
4
,
5
}
S = \{1, 2, 3, 4, 5\}
S
=
{
1
,
2
,
3
,
4
,
5
}
. Find
P
(
6
)
⋅
Q
(
6
)
/
100
P(6) \cdot Q(6) / 100
P
(
6
)
⋅
Q
(
6
)
/100
.
Related theory
Polynomials
Nature and relations of roots
Algebra
Relationship between zeroes and coefficients
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