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Problem
Problem
Passage - 5 (Question 70 to 71): For
a
,
b
∈
R
−
{
0
}
a, b \in R - \{0\}
a
,
b
∈
R
−
{
0
}
, let
f
(
x
)
=
a
x
2
+
b
x
+
a
f(x) = ax^2 + bx + a
f
(
x
)
=
a
x
2
+
b
x
+
a
satisfies
f
(
x
+
7
4
)
=
f
(
7
4
−
x
)
∀
x
∈
R
.
Also the equation
f\left(x + \frac{7}{4}\right) = f\left(\frac{7}{4} - x\right) \forall x \in R. \text{ Also the equation}
f
(
x
+
4
7
)
=
f
(
4
7
−
x
)
∀
x
∈
R
.
Also the equation
f
(
x
)
=
(
7
x
+
a
)
f(x) = (7x + a)
f
(
x
)
=
(
7
x
+
a
)
has only one real and distinct solution. The minimum value of
f
(
x
)
f(x)
f
(
x
)
in
[
0
,
3
2
]
\left[0, \frac{3}{2}\right]
[
0
,
2
3
]
is equal to (a)
−
33
8
-\frac{33}{8}
−
8
33
(b) 0 (c) 4 (d) -2
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