The cubic equation whose roots are the squares of the roots of the equation $x^3-2x^2+3x-4=0$ is

If $\alpha, \beta$ are the roots of the quadratic equation $x^{2}+a x+b=0, (b \neq 0),$ then the quadratic equation whose roots are $\alpha-\frac{1}{\beta}$ and $\beta-\frac{1}{\alpha}$ is:

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3x^2+4x+5=0$,then the cubic equation whose roots are $1+4\alpha$,$1+4\beta$ and $1+4\gamma$ is

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If $\alpha$ and $\beta$ are two real numbers satisfying $\alpha^2 + \beta^2 = 5$ and $3(\alpha^5 + \beta^5) = 11(\alpha^3 + \beta^3)$,then the value of $\alpha \beta$ is:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 6x + \lambda = 0$ and $3\alpha + 2\beta = -20$,then $\lambda = $