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the possible values of a for which e 2x -(a-2)e x +a (a)6 (b)9 (c)12 (d)16

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

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question

e2x– (a-2)ex+ a < 0
Let
t = ex
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
a = \frac{8\pm \sqrt{48}}{2}
a = \frac{8\pm 4\sqrt{3}}{2}
a = 4\pm 2\sqrt{3}
\Rightarrow a\in (4-2\sqrt{3}, 4 + 2\sqrt{3})
So 6 is the correct option.

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