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