If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3x^2-7x+5=0$,then the value of $\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}$ is

If $\alpha_1, \alpha_2$ are the roots of $x^2+ax+1=0$ and $\alpha_3, \alpha_4$ are the roots of $x^2+bx+1=0$,then $(\alpha_1+\alpha_3)(\alpha_2+\alpha_3)(\alpha_1+\alpha_4)(\alpha_2+\alpha_4) = $

Let $\alpha$ and $\beta$ be the roots of the equation $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}$ for $n = 1, 2, 3, \dots$,then:

The value of $c$ for which $|{\alpha ^2} - {\beta ^2}| = \frac{7}{4}$,where $\alpha$ and $\beta$ are the roots of $2{x^2} + 7x + c = 0$,is

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

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

Two candidates attempt to solve the equation $x^2 + px + q = 0$. One starts with a wrong value of $p$ and finds the roots to be $2$ and $6$,and the other starts with a wrong value of $q$ and finds the roots to be $2$ and $-9$. The roots of the original equation are