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

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of their squares,then:

Find $\alpha^4+\beta^4$ if $\alpha, \beta$ are the roots of the equation $x^2+x+1=0$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

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:

If $\alpha, \beta, \gamma$ are roots of $x^3 - 2x^2 + 3x - 2 = 0$,then the value of $\left( \frac{\alpha \beta}{\alpha + \beta} + \frac{\alpha \gamma}{\alpha + \gamma} + \frac{\beta \gamma}{\beta + \gamma} \right)$ is