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Byju's Answer
Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
If α, β and γ...
Question
I
f
α
,
β
a
n
d
γ
are the zeroes of the polynomial,
f
(
x
)
=
x
3
−
p
x
2
+
q
x
−
r
,
t
h
e
n
1
α
β
+
1
β
γ
+
1
γ
α
=
A
−
p
/
r
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B
r
/
p
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C
−
r
/
p
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D
p
/
r
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Solution
The correct option is
D
p
/
r
f
(
x
)
=
x
3
−
p
x
2
+
q
x
−
r
α
,
β
a
n
d
γ
a
r
e
z
e
r
o
e
s
o
f
f
(
x
)
α
+
β
+
γ
=
−
b
a
=
−
(
−
p
)
1
=
p
α
β
+
β
γ
+
γ
α
=
c
a
=
q
1
=
q
α
β
γ
=
−
d
a
=
−
(
−
r
)
1
=
r
1
α
β
+
1
β
γ
+
1
α
γ
=
γ
+
α
+
β
α
β
γ
=
α
+
β
+
γ
α
β
γ
=
p
r
So, option d is correct.
Suggest Corrections
39
Similar questions
Q.
If
α
,
β
,
γ
are non zero roots of
x
3
+
p
x
2
+
q
x
+
r
=
0
, then the equation whose roots are
α
(
β
+
γ
)
,
β
(
γ
+
α
)
,
γ
(
α
+
β
)
Q.
If
α
β
,
α
a
n
d
α
+
β
are the zeroes
of the polynomial,
f
(
x
)
=
x
3
−
3
p
x
2
+
q
x
−
r
,
then which of the following relations
is correct.
Q.
If
α
,
β
,
γ
are the roots of the equation
x
3
+
p
x
2
+
q
x
+
r
=
0
then the coefficient of
x
in the cubic equation whose roots are
α
(
β
+
γ
)
,
β
(
γ
+
α
)
and
γ
(
α
+
β
)
is
Q.
α = 1, β = -1 and γ = 0 then αβ + βγ + γα =
Q.
If
α
,
β
,
γ
are the roots
x
3
−
6
x
−
4
=
0
, then the equation whose roots are
β
γ
+
1
α
,
γ
α
+
1
β
,
α
β
+
1
γ
is
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