Quadratic Root Singular Matrix (Jee Mains) | ExamDuo
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Determinants
Hard
Quadratic Root Singular Matrix
Let
α
be a root of the equation
(
a
−
c
)
x
2
+
(
b
−
a
)
x
+
(
c
−
b
)
=
0
where
a
,
b
,
c
are distinct real numbers such that the matrix
[
α
2
α
1
1
1
1
a
b
c
]
is singular. Then the value of
(
a
−
c
)
2
(
b
−
a
)
(
c
−
b
)
+
(
b
−
a
)
2
(
a
−
c
)
(
c
−
b
)
+
(
c
−
b
)
2
(
a
−
c
)
(
b
−
a
)
is
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D
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