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

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 $p$ and $q$ are non-zero real numbers and $\alpha^3 + \beta^3 = -p$,$\alpha \beta = q$,then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}$ and $\frac{\beta^2}{\alpha}$ is

If $\alpha, \beta$ are the roots of the equation $x^2+bx+c=0$ and $\alpha+h, \beta+h$ are the roots of the equation $x^2+qx+r=0$,then $h$ is equal to

If $c$ and $d$ are the roots of $x^2+ax+b=0$,then a root of $x^2+(4c+a)x+(b+2ac+4c^2)=0$ is

If $\alpha, \beta$ are the roots of $x^2+p x+q=0$,then the values of $\alpha^3+\beta^3$ and $\alpha^4+\alpha^2 \beta^2+\beta^4$ are respectively ...... and ......