If aB are the roots of ar? - 2bx+c=0 then a'B'+a'B'+a'B' -
Answers
Answered by
0
Step-by-step explanation:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
If a,b,c are in GP, then the equation ax
2
+2bx+c=0 and dx
2
+2ex+f=0 have a common root, if
a
d
,
b
e
,
c
f
are in
Medium
Solution
verified
Verified by Toppr
Correct option is A)
We have, ax
2
+2bx+c=0
⇒ax
2
+2
ac
x+c=0(∵b
2
=ac)
⇒(x
a
+
c
)
2
=0
⇒x=−
a
c
This satisfies dx
2
+2ex+f=0
⇒d[
a
c
]+2e[−
a
c
]+f=0
⇒(
a
dc
+f)=2e
a
c
⇒(
a
d
+
c
f
)=2e
ac
1
⇒
a
d
+
c
f
=
b
2e
Therefore,
a
d
,
b
e
,
c
f
arein AP.
Similar questions