If the ratio of the roots of the equation $12x^2 - mx + 5 = 0$ is $2 : 3$,then $m = .....$

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta - \alpha = \sqrt{11}i$ and $\beta^2 - \alpha^2 = 3\sqrt{11}i$, then $(\beta^3 - \alpha^3)^2$ is equal to:

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

If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots will be:

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

If $\alpha$ and $\beta$ are the roots of the equation $a x^2+b x+c=0$ and if $p x^2+q x+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to