Question

If the product of the roots of the equation $x^2-3kx+2e^{2\log k}-1=0$ is $7$, then the roots of the equation are real if $k$ equals

• A. $1$
• B. $2$
• C. $-2$
• D. $\pm 2$

Answer 1

Answer: (B)

$2$

Given quadratic equation
$x^2-3kx+2e^{2\log k}-1=0$
Let $\alpha ,\beta$ be the roots of the eqn
$\alpha \beta =2e^{2\log k}-1$
$\Rightarrow 7=2e^{2\log k}-1$
$\Rightarrow 2e^{2\log k}=8$
$\Rightarrow e^{2\log k}=4$
$\Rightarrow e^{\log k^2}=4$
$\Rightarrow k^2=4$
$\Rightarrow k=-2,2$
But logarithm is not defined for $-2$
So, $k=2$