Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Find the values of ' 
' for which the equation 
has at least one real root.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(5 < a < 
)
The equation can be rewritten as
Let 
= t
Or t = 1 + 
since x 2 + x + 1 = 
+ 
Therefore (x 2 + x + 1) > 
⇒ t 
Now given equation reduces to t 2 - (a - 3) t + (a - 4) = 0
At least one root of the equation must lie in 
Now, t = 
⇒ t = a – 4, 1
For one root to lie in 
we must have 1 < a – 4 < 
⇒ 5 < a < 
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