Question

If all real values of $x$ obtained from the equation $4^x-(a-3)2^x+a-4=0$ are non-positive, then $a$ belongs to

• A. $[4,5]$
• B. $(4,5]$
• C. $[4,5)$
• D. $(4,5)$

Answer 1

Answer: (B)

Given equation can be written as
${\left(2^x\right)}^2-(a-4)2^x-2^x+a-4=0$
$\Rightarrow \left(2^x-1\right)\left(2^x-a+4\right)=0$
$\Rightarrow 2^x=1,2^x=a-4$
Since $x\le 0$ and $2^x=a-4$
$(\because x$ is non-positive)
$\therefore 0<a-4\le 1$
i.e., $4<a\le 5$
i.e., $a\in (4,5]$