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Byju's Answer
Standard XII
Mathematics
Summation by Sigma Method
If α, β and y...
Question
If
α
,
β
a
n
d
γ
are the real roots of the equation
x
3
+
5
x
2
+
9
x
−
6
=
0
. Find the value of
α
2
+
β
2
+
γ
2
.
__
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Solution
We know
(
α
+
β
+
γ
)
2
=
α
2
+
β
2
+
γ
2
+
2
(
α
β
+
β
γ
+
γ
α
)
α
2
+
β
2
+
γ
2
=
(
α
+
β
+
γ
)
2
−
2
(
α
β
+
β
γ
+
γ
α
)
=
(
−
5
)
2
−
2
×
9
= 25 - 18 = 7
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α
,
β
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