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UPSC CDS Math Quadratic Equations and Inequations Questions
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© examsnet.com
Question : 1
Total: 67
If the equations
x
2
+
5
x
+
6
=
0
and
x
2
+
k
x
+
1
=
0
have a common root, then what is the value of ?
[2019 CDS-II]
−
5
2
or
−
10
3
5
2
or
10
3
5
2
or
−
10
3
−
5
2
or
10
3
Validate
Solution:
We know that two equation
a
1
x
2
+
b
1
x
+
c
1
=
0
a
2
x
2
+
b
2
+
c
2
=
0
have common root when
(
c
1
a
2
−
a
1
c
2
)
2
=
(
b
1
c
2
−
c
1
b
2
)
(
a
1
b
2
−
b
1
a
2
)
So, for
x
2
+
5
x
+
6
=
0
and
x
2
+
k
x
+
1
=
0
we have
(
5
)
2
=
(
5
−
6
x
)
(
x
−
5
)
⇒
25
=
−
6
x
2
+
35
x
−
25
⇒
6
x
2
−
35
x
+
50
=
0
⇒
x
=
5
2
or
10
3
© examsnet.com
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