the possible values of a for which e2x-(a-2)ex+a<0 holds for atleast one x bbelongs to (0,infinity) are-(a)6(b)9(c)12(d)16

Ans:
Hello Student,
Please find answer to your question

e^2x– (a-2)e^x+ a < 0
Let
t = e^x
t²– (a – 2)t + a < 0
So the equation does not real roots.
(a – 2)²< 4a
a²+ 4 – 4a < 4a
a²– 8a + 4 < 0




So 6 is the correct option.