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

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3-5x^2+4x-3=0$,then $\sum \alpha \beta(\alpha+\beta)=$

$A$ student notices that the roots of the equation $x^2+bx+a=0$ are each $1$ less than the roots of the equation $x^2+ax+b=0$. Then,$a+b$ is

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x + 4 = 0$,then the equation whose roots are $\alpha^2$ and $\beta^2$ is

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 the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $pq$ is equal to