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AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 4
Total: 160
If
x
is complex, the expression
x
2
+
34
x
−
71
x
2
+
2
x
−
7
takes all values which lie in the interval
(
a
,
b
)
,find the values of
a
and
b
a
=
−
1
,
b
=
1
a
=
1
,
b
=
−
1
a
=
5
,
b
=
9
a
=
9
,
b
=
5
Validate
Solution:
Here we have to find range of
x
2
+
34
x
−
71
x
2
+
2
x
−
7
=
y
(Let)
Then,
x
2
+
34
x
−
71
=
x
2
y
+
2
x
y
−
7
y
⇒
x
2
(
y
−
1
)
+
x
(
2
y
−
34
)
+
(
71
−
7
y
)
=
0
As
x
is complex, discriminant of above equation,
D
≤
0
⇒
(
2
y
−
34
)
2
−
4
(
y
−
1
)
(
71
−
7
y
)
≤
0
$⇒ \;\; 5
⇒
(
a
,
b
)
≡
(
5
,
9
)
© examsnet.com
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