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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If α, β are...
Question
If
α
,
β
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
then show that
1
a
α
+
b
+
1
a
β
+
b
=
b
a
c
Open in App
Solution
If
α
,
β
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
then
a
α
2
+
b
α
+
c
=
0
and
a
β
2
+
b
β
+
c
=
0
α
(
a
α
+
b
)
+
c
=
0
and
β
(
a
β
+
b
)
+
c
=
0
⇒
(
a
α
+
b
)
=
−
c
α
and
(
a
β
+
b
)
=
−
c
β
L.H.S
=
1
a
α
+
b
+
1
a
β
+
b
=
α
−
c
+
β
−
c
=
−
α
−
β
c
=
−
(
α
+
β
)
c
=
−
(
−
b
a
)
c
=
b
a
c
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0
Similar questions
Q.
If
α
,
β
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
, then
α
a
β
+
b
+
β
a
α
+
b
=
Q.
If
α
,
β
are the roots of
a
x
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+
b
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+
c
=
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, then find the equation whose roots are
A)
1
a
2
,
1
β
2
B)
1
a
α
+
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a
β
+
b
C)
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β
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1
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Q.
If
α
and
β
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
. The equation whose roots are as given below.
1
a
α
+
b
,
1
a
β
+
b
is
ac
x
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- bx + 1 = 0. Her
a
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+
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and
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β
+
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Q.
If
α
,
β
are the roots of quadratic equation
a
x
2
+
b
x
+
c
=
0
, then the quadratic equation whose roots are
1
a
α
+
b
,
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a
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, is
Q.
If
α
,
β
are the roots of quadratic equation
a
x
2
+
b
x
+
c
=
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