1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard IX
Mathematics
Zeroes of a Polynomial
Solve the pro...
Question
Solve the problem
I
f
α
,
β
,
γ
a
r
e
t
h
e
r
o
o
t
s
o
f
t
h
e
e
q
u
a
t
i
o
n
x
3
-
3
x
+
11
=
0
t
h
e
n
f
i
n
d
t
h
e
e
q
u
a
t
i
o
n
w
h
o
s
e
r
o
o
t
s
a
r
e
α
+
β
,
β
+
γ
a
n
d
γ
+
α
.
Open in App
Solution
Dear Student,
x
3
-
3
x
+
11
=
0
Comparing
with
ax
3
+
bx
2
+
cx
+
d
=
0
Here
,
a
=
1
b
=
0
c
=
-
3
d
=
11
We
know
that
for
a
cubic
equation
,
α
+
β
+
γ
=
-
b
a
=
-
0
1
=
0
.
.
.
(
i
)
and
,
αβ
+
βγ
+
γα
=
c
a
=
-
3
1
=
-
3
and
,
αβγ
=
-
d
a
=
-
11
1
=
-
11
Now
,
if
there
is
a
cubic
polynomial
of
roots
α
+
β
,
β
+
γ
and
γ
+
α
,
then
it
zeroes
will
be
-
γ
,
-
α
and
-
β
respectively
(
from
eq
i
)
Sum
of
zeroes
=
(
-
γ
)
+
(
-
α
)
+
(
-
β
)
=
-
(
γ
+
α
+
β
)
=
0
Sum
of
product
of
its
two
zeroes
=
(
-
α
)
(
-
β
)
+
(
-
β
)
(
-
γ
)
+
(
-
γ
)
(
-
α
)
or
,
αβ
+
βγ
+
γα
=
-
3
and
,
Product
of
its
zeroes
=
(
-
α
)
(
-
β
)
(
-
γ
)
=
-
αβγ
=
-
(
-
11
)
=
11
So
,
required
polynomial
=
x
3
-
(
Sum
of
zeroes
)
x
2
+
(
Sum
of
product
of
its
two
zeroes
)
x
-
(
Product
of
its
zeroes
)
=
x
3
-
0
x
2
-
3
x
-
11
=
x
3
-
3
x
-
11
Suggest Corrections
0
Similar questions
Q.
If
α
,
β
,
γ
are the roots of
x
3
−
3
x
+
7
=
0
, then the equation whose roots are
α
+
β
−
γ
,
β
+
γ
−
α
,
γ
+
α
−
β
is
Q.
If
α
,
β
,
γ
are the roots of the cubic
x
3
−
p
x
2
+
q
x
−
r
=
0
, find the equations whose roots are
(
β
+
γ
−
α
)
,
(
γ
+
α
−
β
)
,
(
α
+
β
−
γ
)
Q.
If the
α
,
β
,
γ
are the roots of the equation
x
3
+
b
x
2
+
3
x
−
1
=
0
(
α
≤
β
≤
γ
,
α
,
β
,
γ
are in
H
.
P
.) then
Q.
lf
α
,
β
,
γ
are the roots of
x
3
+
2
x
−
3
=
0
, then the transformed equation having the roots
α
β
+
β
α
,
β
γ
+
γ
β
,
γ
α
+
α
γ
is obtained by taking
x
=
Q.
If
α
,
β
,
γ
are the roots of the equation
x
3
−
3
x
+
11
=
0
, then the equation whose roots are
(
α
+
β
)
,
(
β
+
γ
)
and
(
γ
+
α
)
is :
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Adaptive Q11
MATHEMATICS
Watch in App
Explore more
Zeroes of a Polynomial
Standard IX Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app
