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CGP EDU Academic Team
Published on: August 13, 2026
Find all the values of the parameter a for which the equation x(x + 1) (x + a) (x + a + 1) = a 2 has four real roots.
Text Solution
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Sol. The given equation is 
Putting 
, the given equation reduces to 
and 
The given equation will have four real roots if equations (i) and (ii) have each two real roots for which
Now four possibilities arise:
or 
or 
It is clear that 
,
or 
Hence 
or 
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