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NDA Math Quadratic Equations and Inequations
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© examsnet.com
Question : 61
Total: 67
If the sum of the roots of the equation
a
x
2
+
b
x
+
c
=
0
is equal to the sum of their squares,then
[NDA II 2015]
a
2
+
b
2
=
c
2
a
2
+
b
2
=
a
+
b
a
b
+
b
2
=
2
a
c
a
b
−
b
2
=
2
a
c
Validate
Solution:
a
x
2
+
b
x
+
c
=
0
Let the root be α and β.
α
+
β
=
−
b
a
,
α
.
β
=
c
a
⇒
α
+
β
=
α
2
+
β
2
...........(given)
⇒
α
+
β
=
(
α
+
β
)
2
−
2
α
β
⇒
−
b
a
=
(
−
b
a
)
2
−
2
c
a
⇒
b
2
+
a
b
=
2
a
c
© examsnet.com
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