If the equation having the roots as the values obtained by diminishing each root of the equation $x^3-3x^2+2x-1=0$ by $K$ is $x^3-x-1=0$,then $K=$

If $\alpha$ and $\beta$ are roots of $ax^{2}+bx+c=0$,then the equation whose roots are $\alpha^{2}$ and $\beta^{2}$ is

If $\alpha, \beta$,where $\alpha < \beta$,are the roots of the equation $\lambda x^{2} - (\lambda + 3)x + 3 = 0$ such that $\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}$,then the sum of all possible values of $\lambda$ is:

If one root of the equation $ax^2 + bx + c = 0$ is the square of the other,then $a(c - b)^3 = cX$,where $X$ is

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

If the sum of two roots of the equation $x^3-2px^2+3qx-4r=0$ is zero,then the value of $r$ is