Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Equation 
has real roots 
are non-negative).
(i) Minimum non-negative real value of 
is
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CHECK THE SOLUTION.
(i) , (ii) , (iii)
Since, 
roots must be negative. Let the roots be 
. Then,
Now,
or 
Hence, the minimum value of 
is 4 . Similarly,
or 
Hence, the minimum value of 
is 6 . Finally,
Hence, the minimum value of 
is 4 .
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