If $\alpha, \beta$ and $\gamma$ are the roots of ${x^3} + px + q = 0$,then the value of ${\alpha^3} + {\beta^3} + {\gamma^3}$ is equal to

If $(\alpha+\sqrt{\beta})$ and $(\alpha-\sqrt{\beta})$ are the roots of the equation $x^{2}+px+q=0$, where $\alpha, \beta, p$ and $q$ are real, then the roots of the equation $(p^{2}-4q)(p^{2}x^{2}+4px)-16q=0$ are

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\alpha + \beta, \alpha^2 + \beta^2, \alpha^3 + \beta^3$ are in $G.P.$, where $\Delta = b^2 - 4ac$, then:

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then what are the roots of the equation $cx^2 + bx + a = 0$?

Which of the following quadratic equations has real roots $x_1, x_2$ that satisfy the conditions $x_1^2+x_2^2=5$ and $3(x_1^5+x_2^5)=11(x_1^3+x_2^3)$?

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 $\alpha^2+\beta^2+\gamma^2-k=$