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 ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$,then

Let $p$ and $q$ be real numbers such that $p \neq 0, p^3 \neq q$ and $p^3 \neq -q$. If $\alpha$ and $\beta$ are non-zero numbers satisfying $\alpha + \beta = -p$ and $\alpha^3 + \beta^3 = q$,then find the quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

In a triangle $PQR$,$\angle R = \pi / 2$. If $\tan(P/2)$ and $\tan(Q/2)$ are the roots of the quadratic equation $ax^2 + bx + c = 0$,where $a \neq 0$,then which of the following is true?

The equation whose roots are the reciprocals of the roots of the equation $3x^2 - 20x + 17 = 0$ is

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3 - 3x^2 + x + 5 = 0$,then $y = \sum \alpha^2 + \alpha \beta \gamma$ satisfies which of the following equations?