If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 3x + 5 = 0$,then find the quadratic equation whose roots are $(\alpha^2 - 3\alpha + 7)$ and $(\beta^2 - 3\beta + 7)$.

$\alpha, \beta, \gamma$ are the roots of the equation $x^3-10x^2+7x+8=0$. Match the following and choose the correct answer.

Column-$I$	Column-$II$
$A$. $\alpha+\beta+\gamma$	$(1)$ $-\frac{43}{4}$
$B$. $\alpha^2+\beta^2+\gamma^2$	$(2)$ $-\frac{7}{8}$
$C$. $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}$	$(3)$ $86$
$D$. $\frac{\alpha}{\beta\gamma}+\frac{\beta}{\gamma\alpha}+\frac{\gamma}{\alpha\beta}$	$(4)$ $0$
	$(5)$ $10$

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is

If one root of the quadratic equation $x^2 + px + q = 0$ is the square of the other,then:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + x^2 + x + 1 = 0$,then match the items of List-$I$ with those of List-$II$:
List-$I$:
$(i)$ $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma}$
(ii) $\alpha^3 + \beta^3 + \gamma^3$
(iii) $\alpha^4 + \beta^4 + \gamma^4$
(iv) $(\alpha - \beta)^2 + (\beta - \gamma)^2 + (\gamma - \alpha)^2$
List-$II$:
$(A)$ $-1$
$(B)$ $-4$
$(C)$ $1$
$(D)$ $3$
$(E)$ $0$

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