Question

The roots of the equation $4^x-{3.2}^{x+2}+32=0$ are

• A. 1,2
• B. 1,3
• C. 2,3
• D. 1,4

Answer 1

The correct option is C 2,3

$Given$
$4^x-3\cdot 2^{x+2}+32=0$
$\Rightarrow {\left(2^x\right)}^2-3\left(2^x\right)\left(2^2\right)+32=0$
$\Rightarrow {\left(2^x\right)}^2-12\left(2^x\right)+32=0$
$Let{2}^x=t$
$t^2-12t+32=0$
$\Rightarrow (t-4)(t-8)=0$
$t=4,8$
$2^x=8$
$x=3$
$2^x=4$
$x=2$
$Hencerootsare(2,3)$