5
You visited us
5
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Geometric Mean
Given that ...
Question
Given that
α
,
γ
are roots of the equation
A
x
2
−
4
x
+
1
=
0
and
β
,
σ
the roots of the equation
B
x
2
−
6
x
+
1
=
0
, then find the value of (A+B), such that
α
,
β
,
γ
&
σ
are in H.P.
Open in App
Solution
Let
α
=
1
a
,
β
=
1
a
+
d
,
γ
=
1
a
+
2
d
,
σ
=
1
a
+
3
d
So,
α
+
γ
=
1
a
+
1
a
+
2
d
=
2
(
a
+
d
)
a
(
a
+
2
d
)
=
2
α
γ
β
=
4
A
⇒
α
γ
β
=
2
A
Similarly,
β
σ
γ
=
3
A
But,
α
γ
=
1
A
and
β
σ
=
1
B
ie,
β
=
1
2
and
γ
=
1
3
As all of them are in Harmonic Progression,
α
=
1
and
σ
=
1
4
Then,
A
+
B
=
1
α
γ
+
1
β
σ
=
3
+
8
=
11
Suggest Corrections
0
Similar questions
Q.
Given that
α
,
γ
are the roots of equations
A
x
2
- 4x + 1 = 0 and
β
,
γ
the roots of equation
B
x
2
- 6x + 1 = 0. then find the value of (A +B), such that
α
,
β
,
γ
&
δ
are in H.P.
Q.
Given that
α
,
γ
are the roots of the equation
A
x
2
−
4
x
+
1
=
0
and
β
,
δ
the roots of equation,
B
x
2
−
6
x
+
1
=
0
where
α
,
β
,
γ
,
δ
,
are in H.P. Then
Q.
If
α
,
β
,
γ
are the roots of
a
x
3
+
b
x
2
+
c
x
+
d
=
0
and
∣
∣ ∣ ∣
∣
α
β
γ
β
γ
α
γ
α
β
∣
∣ ∣ ∣
∣
=
0
,
α
≠
β
≠
γ
, then find the equation whose roots are
α
+
β
−
γ
,
γ
+
α
−
β
,
β
+
γ
−
α
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.
If α, β, γ are the roots of the equation
x
3
+
4
x
+
1
=
0
,then
(
α
+
β
)
−
1
+
(
β
+
γ
)
−
1
+
(
γ
+
α
)
−
1
=
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
Geometric Progression
MATHEMATICS
Watch in App
Explore more
Geometric Mean
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
Solve
Textbooks
Question Papers
Install app