If x > 0 then the equation x λ nx = a has
(i) no root if –
< a < 0
a > 0
a = – 
a = – 
Text Solution
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Ans.
(i)
Sol. Using graph of y = x λ nx and y = a
y = x λ nx has minimum value at x = 1/e
that is y = –1/e
Hence a < – 
⇒ no root
and – 
< a < 0 ⇒ two root
for a = – 
⇒ one real root
(ii)
Sol. Using graph of y = x λ nx and y = a
y = x λ nx has minimum value at x = 1/e
that is y = –1/e
Hence a < – 
⇒ no root
and – 
< a < 0 ⇒ two root
for a = – 
⇒ one real root
(iii)
Sol. Using graph of y = x λ nx and y = a
y = x λ nx has minimum value at x = 1/e
that is y = –1/e
Hence a < – 
⇒ no root
and – 
< a < 0 ⇒ two root
for a = – 
⇒ one real root
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