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WBJEE 2014 Maths Solved Paper
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© examsnet.com
Question : 56
Total: 80
If a, b and c are positive numbers in a G.P., then the roots of the quadratic equation (
log
e
a
)
x
2
– (2
log
e
b
)x + (
log
e
c
) = 0are
-1 and
log
e
c
log
e
a
1 and
log
e
c
log
e
a
-1 and
log
a
c
1 and
log
c
a
Validate
Solution:
b
2
= ac ⇒
log
e
a
– 2
log
e
b
+
log
e
c
= 0
(
log
e
a
)
x
2
− (2
log
e
b
) x +
log
e
c
= 0
Since, 1 satisfies the equation
Therefore 1 is one root and other root say β
1 . β =
log
e
c
log
e
a
=
log
c
a
β =
log
e
c
log
e
a
=
log
a
c
© examsnet.com
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