If the product of the roots of the equation x | vedclass

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(C) The given quadratic equation is $x^2+4kx+12e^{3\log k}-1=0$. Using the property $e^{\log a} = a$,we have $e^{3\log k} = e^{\log k^3} = k^3$. Thus,

Vedclass · Accepted Answer

$-12$

Vedclass · Answer

(C) The given quadratic equation is $x^2+4kx+12e^{3\log k}-1=0$. Using the property $e^{\log a} = a$,we have $e^{3\log k} = e^{\log k^3} = k^3$. Thus,the equation becomes $x^2+4kx+12k^3-1=0$. The product of the roots of a quadratic equation $ax^2+bx+c=0$ is given by $\frac{c}{a}$. Here,the product is $12k^3-1$. Given that the product of the roots is $323$,we have $12k^3-1 = 323$. $12k^3 = 324$ $\Rightarrow k^3 = 27$ $\Rightarrow k = 3$. The sum of the roots is given by $-\frac{b}{a} = -4k$. Substituting $k=3$,the sum of the roots is $-4(3) = -12$. Therefore,option $C$ is correct.

If the product of the roots of the equation $x^2+4kx+12e^{3\log k}-1=0$ where $k>0$ is $323$,then the sum of its roots is:

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