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Byju's Answer
Standard XII
Mathematics
Properties of Determinants
If α,β and γ ...
Question
If
α
,
β
and
γ
are
the
roots
of
px
3
+
qx
2
+
r
=
0
,
then
the
value
of
⎛
⎜
⎝
αβ
βγ
γα
βγ
γα
αβ
γα
αβ
βγ
∣
∣ ∣ ∣
∣
is
.
A
−
r
p
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B
−
q
p
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C
0
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D
1
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Solution
The correct option is
C
0
For
the
given
equation
px
3
+
qx
2
+
r
=
0
,
Sum
of
product
of
the
roots
taken
two
at
a
time
=
αβ
+
βγ
+
γα
=
0
⎛
⎜
⎝
αβ
βγ
γα
βγ
γα
αβ
γα
αβ
βγ
∣
∣ ∣ ∣
∣
C
1
→
C
1
+
C
2
+
C
3
=
⎛
⎜
⎝
αβ
+
βγ
+
γα
βγ
γα
αβ
+
βγ
+
γα
γα
αβ
αβ
+
βγ
+
γα
αβ
βγ
∣
∣ ∣ ∣
∣
=
(
αβ
+
βγ
+
γα
)
⎛
⎜
⎝
1
βγ
γα
1
γα
αβ
1
αβ
βγ
∣
∣ ∣ ∣
∣
=
0
Suggest Corrections
0
Similar questions
Q.
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=
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,
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∣
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Q.
If
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β
and
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are
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px
3
+
qx
2
+
r
=
0
,
then
the
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⎛
⎜
⎝
αβ
βγ
γα
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αβ
βγ
∣
∣ ∣ ∣
∣
is
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