Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If a 1 < a 2 < a 3 < a 4 < a 5 < a 6 , then the equation (x – a 1 )(x – a 3 )(x–a 5 ) +3(x – a 2 )(x – a 4 )(x–a 6 ) = 0,has –
A
Three real roots
B
A root in (– 
, a 1 )
, a 1 )
C
One root in (a 1 , a 2 )
D
One root in (a 5 , a 6 )
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b, c)
Let f(x) = (x – α 1 ) (x – α 3 ) (x – α 5 ) + 3
(x – α 2 ) (x – α 4 ) (x – α 6 )
f( α 1 ) = – ve, f( α 2 ) = + ve, f( α 3 ) = + ve, f( α 4 ) = – ve
f( α 4 ) = – ve f( α 6 ) = + ve
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