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Byju's Answer
Standard XII
Mathematics
Relation between AM,GM,HM for 2 Numbers
The value of ...
Question
The value of
′
a
′
for which the sum of the squares of the roots of
2
x
2
−
2
(
a
−
2
)
x
−
a
−
1
=
0
is least is-
A
1
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B
3
/
2
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C
2
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D
−
1
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Solution
The correct option is
B
3
/
2
2
x
2
−
2
(
a
−
2
)
x
−
a
−
1
=
0
⇒
2
x
2
−
2
(
a
−
2
)
x
−
(
a
+
1
)
=
0
let
α
,
β
be the roots of equation. Then we can write
⇒
α
+
β
=
−
−
2
(
a
−
2
)
2
=
a
−
2
⇒
α
β
=
−
(
a
+
1
)
2
⇒
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
⇒
α
2
+
β
2
=
(
a
−
2
)
2
−
(
2
×
−
(
a
+
1
)
2
)
⇒
α
2
+
β
2
=
(
a
−
2
)
2
+
a
+
1
⇒
α
2
+
β
2
=
a
2
+
4
−
4
a
+
a
+
1
⇒
α
2
+
β
2
=
a
2
−
3
a
+
5
Let
α
2
+
β
2
=
S
Given that
S
is minimum
Therefore
⇒
d
S
d
a
=
0
⇒
d
d
a
(
a
2
−
3
a
+
5
)
=
0
⇒
2
a
−
3
=
0
⇒
a
=
3
2
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0
Similar questions
Q.
The value of
p
for which the sum of the squares of the roots of
2
x
2
−
2
(
p
−
2
)
x
−
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−
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=
0
is least is
Q.
The value of
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assume the least value is -
Q.
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−
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−
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assume the least value is -
Q.
The value of
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for which the sum of the square of the roots of
x
2
−
(
a
−
2
)
x
−
(
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)
=
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Q.
Find all values of
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is equal to the sum of the squares of its roots.
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