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

If $\alpha, \beta$ are the roots of the equation $Ax^2 + Bx + C = 0$ and $\alpha^2, \beta^2$ are the roots of the equation $x^2 + px + q = 0$,then $p = \dots$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 5x^2 - 7x - 1 = 0$,then find the equation whose roots are $\alpha\beta, \beta\gamma, \gamma\alpha$.

If the roots of the equation $Ax^2 + Bx + C = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2, \beta^2$,then the value of $p$ is:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+ax^2+bx+c=0$,then the roots of the equation $x^3+(2b-a^2)x^2+(b^2-2ac)x-c^2=0$ are

If $\alpha$ and $\beta$ are the roots of $x^2+7x+3=0$ and $\frac{2\alpha}{3-4\alpha}, \frac{2\beta}{3-4\beta}$ are the roots of $ax^2+bx+c=0$ and $GCD(a, b, c) = 1$,then $a+b+c=$