Question

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

• A. roots are integers and positive
• B. roots are integers and negative
• C. roots are rational not integers
• D. roots are irrational

Answer 1

The correct option is D roots are irrational

$x^2-3kx+2e^{\log k}-1=0$

$a=1,b=-3k$ and $c=2e^{\log k}-1$

Product of roots given $\frac{c}{a}=7$

$\Rightarrow \frac{c}{a}=7=\frac{2e^{\log k}-1}{1}$

$\Rightarrow 7+1=2e^{{\log }_{e}k}$ ($e^{{\log }_{e}a}=a^{{\log }_{e}e}=a$)

$\Rightarrow 4=k$

$D=144-4\left(7\right)=116$ is not a perfect square.

$\Rightarrow$ Roots are irrational number