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Byju's Answer
Standard XII
Mathematics
Relations between Roots and Coefficients
If α and β ar...
Question
If
α
and
β
are the roots of
a
x
2
+
b
x
+
c
=
0
(
b
≠
0
)
and
α
β
<
0.
Then the roots of
α
(
x
−
β
)
2
+
β
(
x
−
α
)
2
=
0
are
A
real and of opposite sign
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B
negative
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C
non-real
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D
positive
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Solution
The correct option is
A
real and of opposite sign
b
≠
0
⇒
α
+
β
≠
0
For
α
(
x
−
β
)
2
+
β
(
x
−
α
)
2
=
0
⇒
(
α
+
β
)
x
2
−
4
α
β
x
+
α
β
(
α
+
β
)
=
0
Δ
=
16
α
2
β
2
−
4
α
β
(
α
+
β
)
2
>
0
(
∵
α
β
<
0
)
product of roots
=
α
β
(
α
+
β
)
(
α
+
β
)
=
α
β
<
0
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