The sum of the roots of a quadratic equation is $2$ and the sum of their cubes is $98$. Then the equation is:

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

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

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 2(m^2 + 1)x + m^4 + m^2 + 1 = 0$,then find the value of $\alpha^2 + \beta^2$.

The equation $x^5-5x^3+5x^2-1=0$ has three equal roots. If $\alpha$ and $\beta$ are the other two roots of this equation,then $\alpha+\beta+\alpha\beta=$

If $\alpha, \beta, \gamma$ are the roots of $x^3+2x^2-3x-1=0$,then $\alpha^{-2}+\beta^{-2}+\gamma^{-2}=$

Sachin and Rahul solve a quadratic equation. Sachin makes a mistake in writing the constant term and obtains roots $(4, 3)$. Rahul makes a mistake in writing the coefficient of $x$ and obtains roots $(3, 2)$. What are the correct roots of the equation?