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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If α, β be ...
Question
If
α
,
β
be two zeroes of the quadratic polynomial
a
x
2
+
b
x
−
c
=
0
, then
α
2
β
+
β
2
α
=
_______.
A
b
2
−
2
a
c
a
2
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B
3
a
b
c
−
b
3
c
3
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C
3
a
b
c
−
b
3
a
2
c
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D
b
3
+
3
a
b
c
a
2
c
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Solution
The correct option is
D
b
3
+
3
a
b
c
a
2
c
Sum of the roots of the given equation
=
α
+
β
=
−
b
a
...(1)
Product of the roots of the given equation
=
α
β
=
−
c
a
....(2)
α
2
β
+
β
2
α
=
α
3
+
β
3
α
β
=
(
α
+
β
)
(
α
2
−
α
β
+
β
2
)
α
β
=
(
α
+
β
)
(
(
α
+
β
)
2
−
2
α
β
−
α
β
)
α
β
=
(
α
+
β
)
(
(
α
+
β
)
2
−
3
α
β
)
α
β
....(3)
Substituting (1),(2) in (3), we get
α
2
β
+
β
2
α
=
(
−
b
/
a
)
(
(
−
b
/
a
)
2
−
3
(
−
c
/
a
)
)
−
c
/
a
=
b
c
[
b
2
a
2
+
3
c
a
]
=
b
c
b
2
+
3
a
b
c
a
2
=
b
3
+
3
a
b
c
a
2
c
Suggest Corrections
1
Similar questions
Q.
If
α
,
β
are the roots of
a
x
2
+
b
x
+
c
=
0
then match the elements of list I with elements of list II:
List I
List II
A)
α
β
+
β
α
=
1)
c
2
a
2
B)
α
2
+
β
2
α
−
2
+
β
−
2
=
2)
c
5
[
3
a
b
c
−
b
3
]
a
8
C)
α
3
+
β
3
3)
b
2
−
2
a
c
a
c
D)
α
5
β
8
+
α
8
β
5
=
4)
3
a
b
c
−
b
3
a
3
The correct match from List-I to List-II:
A
,
B
,
C
,
D
Q.
If one root of the quadratic equation ax
2
+ bx + c = 0 is the square of the other show that
b
3
+
a
2
c
+
a
c
2
=
3
a
b
c