Question

If the product of the roots of the equation $x^2-2\sqrt{2}kx+2e^{2logk}-1=0$ is $31$ then the roots of the equation are real for $k$ =

• A. -4
• B. 1
• C. 4
• D. 0

Answer 1

Answer: (C)

Given, $x^2-2\sqrt{2k}x+2e^{2\log k}-1=0$
$\therefore$ Product of roots $=2e^{2\log k}-1$
$=31$ (given)
$\Rightarrow 2e^{2\log k}=32$
$\Rightarrow e^{\log k^2}=16$
$\Rightarrow k^2=16$
$\Rightarrow k=\pm 4$
But $k=-4,\log k$ is not defined.
Hence, required value of $k$ is $4$ .