For what value of $a$, the sum of the squares of the roots of the equation $x^2-(a-2)x-a+1=0$ will have the least value?

If $8$ and $2$ are the roots of ${x^2} + ax + \beta = 0$ and $3$ and $3$ are the roots of ${x^2} + \alpha x + b = 0$,then the roots of ${x^2} + ax + b = 0$ are

If the equation $x^{2}-cx+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+ax+b=0,$ where $a^{2}>4b,$ then the roots of $x^{2}-4bx+2b^{2}-c=0$ will be

If $\alpha$ and $\beta$ are the roots of $x^{2}-ax+b^{2}=0$,then $\alpha^{2}+\beta^{2}$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+x^2+x+r=0$ and $\alpha^3+\beta^3+\gamma^3=5$,then $r=$

If the roots of the equation $x^2 + bx + ac = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + ax + bc = 0$ are $\alpha, \gamma$,then what are the values of $\alpha, \beta, \gamma$ respectively?