If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + x + 1 = 0$,then the value of $\alpha^3 \beta^3 \gamma^3$ is:

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $a x^2+b x+c=0$. Match the conditions in List-$I$ with the corresponding relations in List-$II$.

List-$I$	List-$II$
$(i) \alpha = \beta$	$(A) (ac^2)^{1/3} + (a^2c)^{1/3} + b = 0$
$(ii) \alpha = 2\beta$	$(B) 2b^2 = 9ac$
$(iii) \alpha = 3\beta$	$(C) b^2 = 6ac$
$(iv) \alpha = \beta^2$	$(D) 3b^2 = 16ac$
	$(E) b^2 = 4ac$
	$(F) (ac^2)^{1/3} + (a^2c)^{1/3} = b$

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

If the difference between the roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is the same,and $a \neq b$,then:

If $\alpha, \beta$ are the roots of $x^2 - 2x + 4 = 0$,then $\alpha^5 + \beta^5$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3+x^2-13x+6=0$,then $\alpha^3+\beta^3+\gamma^3=$