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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 1 Questions
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© examsnet.com
Question : 4
Total: 100
The value of
λ
such that sum of the squares of the roots of the quadratic equation,
x
2
+
(
3
−
λ
)
x
+
2
=
λ
has the least value is:
[Jan. 10, 2019 (II)]
15
8
1
4
9
2
Validate
Solution:
The given quadratic equation is
x
2
+
(
3
−
λ
)
x
+
2
=
λ
Sum of roots
=
α
+
β
=
λ
−
3
Product of roots
=
α
β
=
2
−
λ
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
=
(
λ
−
3
)
2
−
2
(
2
−
λ
)
=
λ
2
−
4
λ
+
5
=
(
λ
−
2
)
2
+
1
For least
(
α
2
+
β
2
)
λ
=
2
© examsnet.com
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