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Problem
Problem
If
f
(
x
)
=
(
x
−
a
)
(
x
−
b
)
f(x) = (x-a)(x-b)
f
(
x
)
=
(
x
−
a
)
(
x
−
b
)
for
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
, then minimum number of roots of equation
π
(
f
′
(
x
)
)
2
cos
(
π
f
(
x
)
)
+
sin
(
π
f
(
x
)
)
⋅
f
′
′
(
x
)
=
0
\pi(f'(x))^2 \cos(\pi f(x)) + \sin(\pi f(x)) \cdot f''(x) = 0
π
(
f
′
(
x
)
)
2
cos
(
π
f
(
x
))
+
sin
(
π
f
(
x
))
⋅
f
′′
(
x
)
=
0
in
(
α
,
β
)
(\alpha, \beta)
(
α
,
β
)
, where
f
(
α
)
=
+
3
=
f
(
β
)
f(\alpha) = +3 = f(\beta)
f
(
α
)
=
+
3
=
f
(
β
)
is ..... (here,
α
<
a
<
b
<
β
\alpha < a < b < \beta
α
<
a
<
b
<
β
)
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