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Byju's Answer
Standard X
Mathematics
Nature of Roots
If α, β are...
Question
If
α
,
β
are the roots of the equation
x
2
+
x
−
15
=
0
then find
1
α
2
+
1
β
2
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Solution
Here
a
=
1
,
b
=
1
,
c
=
−
15
Sum of the roots
=
α
+
β
=
−
b
a
=
−
1
1
=
−
1
Product of the roots
=
α
β
=
c
a
=
−
15
1
=
−
15
Consider,
1
α
2
+
1
β
2
=
α
2
+
β
2
α
2
β
2
=
(
α
+
β
)
2
−
2
α
β
(
α
β
)
2
=
(
−
1
)
2
−
2
×
−
15
(
−
15
)
2
=
1
+
30
225
=
31
225
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0
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