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TS EAMCET 11-Sep-2020 Shift 1 Solved Paper
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© examsnet.com
Question : 11
Total: 160
p
and
q
are two roots of the equation
x
2
+
7
x
+
3
=
0
. If
3
p
1
−
2
p
,
3
q
1
−
2
q
are the roots of
l
x
2
+
m
x
+
n
=
0
and the greatest common divisor of
l
,
m
,
n
is 1 , then
l
−
m
+
n
=
11
-3
-1
12
Validate
Solution:
It is given that
p
and
q
are roots of quadratic equation
x
2
+
7
x
+
3
=
0
To find the quadratic equation whose roots are
3
p
1
−
2
p
and
3
q
1
−
2
q
, put
3
p
1
−
2
p
=
x
3
p
=
x
−
2
p
x
⇒
p
=
x
3
+
2
x
∵
p
is the root of equation
x
2
+
7
x
+
3
=
0
, so
(
x
3
+
2
x
)
2
+
7
(
x
3
+
2
x
)
+
3
=
0
⇒
x
2
+
7
x
(
3
+
2
x
)
+
3
(
3
+
2
x
)
2
=
0
⇒
27
x
2
+
57
x
+
27
=
0
⇒
9
x
2
+
19
x
+
9
=
0
So, on comparing with
l
x
2
+
m
x
+
n
=
0
, we get
l
=
9
,
m
=
19
and
n
=
9
∴
l
−
m
+
n
=
9
−
19
+
9
=
−
1
© examsnet.com
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