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Byju's Answer
Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
If α, β, γ ...
Question
If
α
,
β
,
γ
are the zeroes of the cubic polynomial
a
x
3
+
b
x
2
+
c
x
+
d
=
0
, then
α
+
β
+
γ
=
−
b
a
.
A
True
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B
False
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C
Can't be determined
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D
None of the above
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Solution
The correct option is
A
True
We know that if
α
,
β
,
γ
are the zeroes of
a
x
3
+
b
x
2
+
c
x
+
d
, then
α
+
β
+
γ
=
−
b
a
,
α
β
+
β
γ
+
γ
α
=
c
a
,
α
β
,
γ
=
−
d
a
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2
Similar questions
Q.
If
α
,
β
and
γ
are the zeroes of the polynomial
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
, then
1
α
+
1
β
+
1
γ
is _____.
Q.
If
α
,
β
,
γ
are the zeros of a polynomial
P
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
(
a
≠
0
)
then
1
α
+
1
β
+
1
γ
=
..............
Q.
α
,
β
&
γ
are the zeroes of cubic polynomial
P
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
,
(
a
≠
0
)
then product of their zeroes
[
α
.
β
.
γ
]
=
.................
Q.
If
α
,
β
,
γ
are zeros of the polynomial
a
x
3
+
b
x
2
+
c
x
+
d
, then
α
β
γ
=
Q.
If
α
,
β
,
γ
are the zeroes of a cubic polynomial
a
x
3
+
b
x
2
+
c
x
+
d
, then the sum of zeroes is equal to
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