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Byju's Answer
Standard X
Mathematics
Relationship Between Zeroes and Coefficients of a Cubic Polynomial
α, β γ ar...
Question
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
]
=
.................
A
−
b
a
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B
c
a
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C
a
b
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D
−
d
a
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Solution
The correct option is
C
−
d
a
α
,
β
and
γ
are zeros of
P
(
x
)
Then,
α
⋅
β
⋅
γ
=
−
The constant term
The coefficient of
x
3
=
−
d
a
Hence, the answer is
−
d
a
.
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1
Similar questions
Q.
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
.
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.
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
Q.
Assertion :If
α
,
β
,
γ
are the zeroes of
x
3
−
2
x
2
+
q
x
−
r
and
α
+
β
=
0
, then
2
q
=
r
Reason: 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
Q.
If
α
,
β
,
γ
are the zones of a cubic polynomial
a
x
3
+
b
x
2
+
c
x
+
d
, then ________
=
c
a
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