Question

If the product of the roots of the equation $x^2-5x+4^{lo{g}_2\lambda }=0$ is $8$, then $\lambda$ is

• A. $\pm 2\sqrt{2}$
• B. $2\sqrt{2}$
• C. $3$
• D. none of these

Answer 1

The correct option is B $2\sqrt{2}$

The product of both the roots $\alpha \beta =4^{lo{g}_2\lambda }=8$
$\Rightarrow 2^{2lo{g}_2\lambda }=2^{lo{g}_2{\lambda }^2}$=8
$\Rightarrow {\lambda }^2=8$
$\Rightarrow \lambda =2\sqrt{2}$