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Let be 10 real zeros
MATHEMATICS · Subjective · ISC · Mathematics · Physics · Algebra
Problem
Let
x
,
x
1
,
x
2
,
x
3
,
x
4
,
…
,
x
8
x, x_1, x_2, x_3, x_4, \dots, x_8
x
,
x
1
,
x
2
,
x
3
,
x
4
,
…
,
x
8
be 10 real zeros, of the polynomial
P
(
x
)
=
x
10
+
a
x
2
+
b
x
+
c
P(x) = x^{10} + ax^2 + bx + c
P
(
x
)
=
x
10
+
a
x
2
+
b
x
+
c
where
a
,
b
,
c
∈
R
a, b, c \in \mathbb{R}
a
,
b
,
c
∈
R
. If the value of
Q
(
x
1
)
=
p
q
Q(x_1) = \frac{p}{q}
Q
(
x
1
)
=
q
p
, where
p
p
p
and
q
q
q
are coprime to each other. If
Q
(
x
)
=
(
x
−
x
2
)
(
x
−
x
3
)
…
(
x
−
x
8
)
Q(x) = (x - x_2)(x - x_3) \dots (x - x_8)
Q
(
x
)
=
(
x
−
x
2
)
(
x
−
x
3
)
…
(
x
−
x
8
)
and
x
1
=
1
2
x_1 = \frac{1}{2}
x
1
=
2
1
, then the value of
q
−
p
q - p
q
−
p
is .....
Related theory
Polynomials
Higher-Order Derivatives
Quadratic Equations
Polynomial Functions
Numerical Methods
Differentiation Rules
Zeroes of a polynomial
Square numbers and their properties
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