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NDA Math Quadratic Equations and Inequations
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© examsnet.com
Question : 66
Total: 67
If α and β are the roots of the equation
a
x
2
+
b
x
+
c
=
0
, where a ≠ 0, then
(
a
α
+
b
)
(
a
β
+
b
)
is equal to
[NDA I 2014]
ab
bc
ca
abc
Validate
Solution:
a
x
2
+
b
x
+
c
=
0
α
+
β
=
−
b
a
and
α
β
=
c
a
Now,
(
a
α
+
b
)
(
a
β
+
b
)
=
a
2
α
β
+
a
b
(
α
+
β
)
+
b
2
=
a
2
c
a
+
a
b
(
−
b
a
)
+
b
2
=
a
c
−
b
2
+
b
2
=
a
c
© examsnet.com
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