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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
If α ,β are...
Question
If
α
,
β
are the roots of
x
2
−
p
x
+
q
=
0
, find the value of
(1)
α
2
+
β
2
(2)
α
3
+
β
3
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Solution
Given that
α
,
β
are roots of equation
x
2
−
p
x
+
q
=
0
We know that
α
+
β
=
p
and
α
β
=
q
⇒
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
=
p
2
−
2
q
⇒
α
3
+
β
3
=
(
α
+
β
)
3
−
3
α
β
(
α
+
β
)
=
p
3
−
3
q
p
=
p
(
p
2
−
3
q
)
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