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Problem
Problem
Let
P
(
x
)
=
x
10
+
a
2
x
8
+
a
3
x
6
+
a
4
x
4
+
a
5
x
2
P(x) = x^{10} + a_2x^8 + a_3x^6 + a_4x^4 + a_5x^2
P
(
x
)
=
x
10
+
a
2
x
8
+
a
3
x
6
+
a
4
x
4
+
a
5
x
2
be a polynomial with real coefficients. If
P
(
1
)
=
1
P(1) = 1
P
(
1
)
=
1
and
P
(
2
)
=
−
5
P(2) = -5
P
(
2
)
=
−
5
, then the minimum number of distinct real zeroes of
P
(
x
)
P(x)
P
(
x
)
is (a) 5 (b) 6 (c) 7 (d) 8
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