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the cubic equation whose roots are the am gm and h
Question:
The cubic equation whose roots are the AM, GM and HM of the roots of x
2
- 2px + q
2
= 0 is
WBJEE
Updated On:
Apr 27, 2024
(A) (x - p)(x - q)(x - p - q) = 0
(B) (x - p)(x - |q|)(px - q
2
) = 0
(C)
x
3
−
(
p
+
|
q
|
+
q
2
p
)
x
2
+
(
p
|
q
|
+
q
2
+
|
q
|
3
p
)
x
−
|
q
|
3
=
0
(D) None of these
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Verified By Collegedunia
The Correct Option is
B,
C
Solution and Explanation
Explanation:
α
+
β
=
2
p
,
α
β
=
q
2
∴
AM
of roots
=
p
,
GM
of roots
=
|
q
|
,
HM
of roots
=
2
α
β
α
+
β
=
2
q
2
2
p
∴
The cubic equation is
(
x
−
p
)
(
x
−
|
q
|
)
(
x
−
q
2
p
)
=
0
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