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Mathematics
Mathematics
Problem
If
f
(
x
)
f(x)
f
(
x
)
,
g
(
x
)
g(x)
g
(
x
)
and
h
(
x
)
h(x)
h
(
x
)
are three polynomials of degree 2, then prove that
η
(
x
)
=
∣
f
(
x
)
g
(
x
)
h
(
x
)
f
′
(
x
)
g
′
(
x
)
h
′
(
x
)
f
′
′
(
x
)
g
′
′
(
x
)
h
′
′
(
x
)
∣
\eta(x) = \left|\begin{matrix} f(x) & g(x) & h(x) \\ f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \end{matrix}\right|
η
(
x
)
=
f
(
x
)
f
′
(
x
)
f
′′
(
x
)
g
(
x
)
g
′
(
x
)
g
′′
(
x
)
h
(
x
)
h
′
(
x
)
h
′′
(
x
)
is a constant polynomial.
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