Published by:
CGP EDU Academic Team
Published on: August 14, 2026
is the necessary and sufficient condition for a particular real number 
to lie between the roots of a quadratic equation 
, where 
. Again if 
, then exactly one of the roots will lie between 
and 
.
(i) If 
, then
A
one root of 
is positive, the other is negative
one root is less than 0 , the other is greater than 1
one root is less than 0 , the other is greater than 1
is positive, the other is negative one root is less than 0 , the other is greater than 1
one root is less than 0 , the other is greater than 1
B
exactly one of the roots of 
lies in (-1,1)
exactly one of the roots lies in
one root lies in
and other in 
lies in (-1,1) exactly one of the roots lies in
one root lies in
and other in C
1 lies between the roots of 
both the roots lie in
both the roots lie in
both the roots lie in
both the roots lie in
D
both the roots of 
are less than 1
(ii) If
, then
at least one of the roots lies in
(iii) If
, then
one root lies in ( 0,1 ) and other in (
)
are less than 1 (ii) If
, then at least one of the roots lies in
(iii) If
, then one root lies in ( 0,1 ) and other in (
)
Text Solution
Verified by ExpertsThe correct answer is:
B
(i) 
So, there is exactly one root in 
.
(ii) a 
and 
and 
Hence, both the numbers 0 and 1 lie between the roots.
(iii) 
and 
and 
Hence, exactly one root lies in 
and 0 lies between the roots.
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