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Byju's Answer
Standard X
Mathematics
Discriminant
If α, β be th...
Question
If
α
,
β
be the real roots of the equation
x
2
+
a
x
+
1
=
0
.Then the minimum value of
α
2
+
β
2
is
A
1
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B
4
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C
0
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D
2
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Solution
The correct option is
D
2
α
+
β
=
−
a
,
α
×
β
=
1
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
α
2
+
β
2
=
a
2
−
2
As the roots are real.
So,
a
2
−
4
≥
0
a
2
≥
4
So minimum value of
α
2
+
β
2
=
4
−
2
=
2
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0
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