If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-4x^2-9x+36=0$ such that $\alpha+\beta=0$,then $\alpha^2+2\beta^2+3\gamma^2=$

If the roots of the equations $ax^2 + bx + c = 0$ and $px^2 + qx + r = 0$ are $\alpha_1, \alpha_2$ and $\beta_1, \beta_2$ respectively,and the system of linear equations $\alpha_1y + \alpha_2z = 0$ and $\beta_1y + \beta_2z = 0$ has a non-zero solution,then which of the following is true?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-12x^2+kx-18=0$ and one of them is thrice the sum of the other two roots,then $\alpha^2+\beta^2+\gamma^2-k=$

If $\alpha, \beta$ and $\gamma$ are roots of the equation $x^3+4x-19=0$,then the value of $\frac{\alpha^3}{19-4\alpha}+\frac{\beta^3}{19-4\beta}+\frac{\gamma^3}{19-4\gamma}$ is equal to

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is

If the coefficients of the equation whose roots are $k$ times the roots of the equation $x^3+\frac{1}{4} x^2-\frac{1}{16} x+\frac{1}{144}=0$ are integers,then a possible value of $k$ is