If the product of the roots of $9x^3 + 112x^2 - 120x + a = 0$ is $12$,then the value of '$a$' is

The cubic equation whose roots are the squares of the roots of the equation $12x^3-20x^2+x+3=0$ is

If $\alpha, \beta, \gamma$ are the roots of $x^3-6x^2+11x-6=0$,then the equation having the roots $\alpha^2+\beta^2, \beta^2+\gamma^2$ and $\gamma^2+\alpha^2$ is

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

If $\alpha$ and $\beta$ are two roots of the equation $x^{2}-64x+256=0$,then the value of $\left(\frac{\alpha^{3}}{\beta^{5}}\right)^{\frac{1}{8}}+\left(\frac{\beta^{3}}{\alpha^{5}}\right)^{\frac{1}{8}}$ is

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are: