1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Existence of Limit
Solve this: ...
Question
Solve this:
21
.
I
f
α
,
β
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
2
-
p
x
+
q
=
0
,
t
h
e
n
f
i
n
d
t
h
e
q
u
a
d
r
a
t
i
c
e
q
u
a
t
i
o
n
t
h
e
r
o
o
t
s
o
f
w
h
i
c
h
a
r
e
α
2
-
β
2
α
3
-
β
3
a
n
d
α
3
β
2
+
α
2
β
3
.
Open in App
Solution
Dear student
Given
:
α
and
β
are
roots
of
x
2
-
px
+
q
=
0
α
+
β
=
-
coeff
.
of
x
coeff
.
of
x
2
=
-
-
p
1
=
p
αβ
=
constant
term
coeff
.
of
x
2
=
q
1
=
q
We
know
that
α
+
β
2
=
α
2
+
β
2
+
2
αβ
α
2
+
β
2
=
p
2
-
2
q
and
α
-
β
2
=
α
2
+
β
2
-
2
αβ
=
p
2
-
2
q
-
2
q
=
p
2
-
4
q
So
,
α
-
β
=
±
p
2
-
4
q
We
want
to
find
the
quadratic
equation
whose
roots
are
:
α
2
-
β
2
α
3
-
β
3
and
α
3
β
2
+
α
2
β
3
let
S
and
P
be
the
sum
and
product
of
roots
respectively
.
S
=
α
2
-
β
2
+
α
3
-
β
3
+
α
3
β
2
+
α
2
β
3
S
=
α
+
β
α
-
β
+
α
-
β
α
2
+
β
2
+
αβ
+
α
2
β
2
α
+
β
Case
I
when
α
-
β
=
p
2
-
4
q
S
=
p
×
p
2
-
4
q
+
p
2
-
4
q
p
2
-
2
q
+
q
+
q
2
p
=
p
p
2
-
4
q
+
p
2
-
4
q
p
2
-
2
q
+
q
+
q
2
p
=
p
2
-
4
q
p
+
p
2
-
q
+
pq
2
and
P
=
α
2
-
β
2
α
3
-
β
3
α
2
β
2
α
+
β
=
α
+
β
α
-
β
α
-
β
α
2
+
β
2
+
αβ
α
2
β
2
α
+
β
=
p
p
2
-
4
q
p
2
-
q
q
2
p
=
p
2
q
2
p
2
-
4
q
p
2
-
q
So
,
required
polynomial
is
=
x
2
-
Sx
+
P
=
x
2
-
p
2
-
4
q
p
+
p
2
-
q
+
pq
2
x
+
p
2
q
2
p
2
-
4
q
p
2
-
q
Similarly
try
when
α
-
β
=
-
p
2
-
4
q
Regards
Suggest Corrections
0
Similar questions
Q.
If
α
,
β
are the roots of
x
2
−
p
x
+
q
=
0
, then the product of the roots of the quadratic equation whose roots are
α
2
−
β
2
and
α
3
−
β
3
is
Q.
If
α
,
β
are the roots of the quadratic equation
x
2
+
p
x
+
q
=
0
, then the values of
α
3
+
β
3
and
α
4
+
α
2
β
2
+
β
4
are respectively
Q.
If
α
,
β
are the roots of the equation
x
2
−
p
x
+
q
=
0
,
prove that
log
e
(
1
+
p
x
+
q
x
2
)
=
(
α
+
β
)
x
−
α
2
+
β
2
2
x
2
+
α
3
+
β
3
3
x
3
+
.
.
.
Q.
If
α
,
β
are the roots of
x
2
−
p
x
+
q
=
0
, find the value of
(1)
α
2
+
β
2
(2)
α
3
+
β
3
Q.
If
α
,
β
are the roots of the equation
x
2
−
p
x
+
q
=
0
, then the quadratic equation whose roots are
(
α
2
−
β
2
)
(
α
3
−
β
3
)
and
(
α
3
β
2
+
α
2
β
3
)
:
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
Introduction to Limits
MATHEMATICS
Watch in App
Explore more
Existence of Limit
Standard XII 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
