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Question
Mathematics
The minimum value of the sum of the squares of the roots of x2+(3-a) x+1=2 a is:
Q. The minimum value of the sum of the squares of the roots of
x
2
+
(
3
−
a
)
x
+
1
=
2
a
is:
102
0
JEE Main
JEE Main 2022
Complex Numbers and Quadratic Equations
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A
4
B
5
C
6
D
8
Solution:
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
let
f
(
a
)
=
(
3
−
a
)
2
−
2
(
1
−
2
a
)
f
(
a
)
=
a
2
−
2
a
+
7
f
(
a
)
=
(
a
−
1
)
2
+
6
f
(
a
)
)
min.
=
6