If $a$ and $b$ are the roots of the equation $y^2+y+1=0$,then the value of $a^4+b^4+a^{-1}b^{-1}$ is

Let $\alpha$ and $\beta$ be the roots of the equation $px^2+qx-r=0$,where $p \neq 0$. If $p, q,$ and $r$ are the consecutive terms of a non-constant $G$.$P$. and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$,then the value of $(\alpha-\beta)^2$ is:

If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3x^3-6x^2+2x-4=0$,then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$.

If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$,then the value of $\alpha^6+\beta^6$ is

If the product of roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ will be

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity,then $b + c$ is equal to