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VITEEE 2011 Solved Paper
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© examsnet.com
Question : 104
Total: 120
If α, β and γ are the roots of
x
3
+
a
x
2
+b = 0, then the value of
|
α
β
γ
β
γ
α
γ
α
β
|
is
−
a
3
a
3
- 3b
a
3
a
2
- 3b
Validate
Solution:
α, β . γ are the roots of given equation,
Therefore α + β + γ = - a
αβ + βγ + γα = 0
and αβγ = - b
Now,
|
α
β
γ
β
γ
α
γ
α
β
|
= - (α + β + γ)
(
α
2
+
β
2
+
γ
2
- αβ - βγ - γα)
= - (α + β + γ) [
(
α
+
β
+
γ
)
2
- 3 (αβ + βγ γα)]
= - (- a)
(
a
2
−
0
)
=
a
3
© examsnet.com
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