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UPSC 2017 CDS I Math Paper
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© examsnet.com
Question : 3
Total: 100
If
α
and
β
are the roots of the quadratic equation
2
x
2
+
6
x
+
k
=
0
, where
k
<
0
, then what is the maximum value of
α
β
+
β
α
?
[2017 CDS-I]
2
-2
9
-9
Validate
Solution:
α
+
β
=
−
3
and
α
β
=
k
2
α
β
+
β
α
=
α
2
+
β
2
α
β
=
(
α
+
β
)
2
−
2
α
β
α
β
=
9
−
k
(
k
2
)
=
18
k
−
2
Here
α
β
+
β
α
cannot be positive.
Here we see that the minimum is the value of k, the maximum is the value attained by expression
18
k
−
2
i.e., when
k
→
−
∞
then maximum value of
α
β
+
β
α
is
−
2
© examsnet.com
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