If $\alpha, \beta, \gamma$ are the roots of $x^3-x+1=0$,then $\frac{1+\alpha}{1-\alpha}+\frac{1+\beta}{1-\beta}+\frac{1+\gamma}{1-\gamma}=$

If the roots of the equation $ax^2 + ax + c = 0$ are in the ratio $p:q$,then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} = $

If $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^{2}+bx+c=0$ and $3b^{2}=16ac$, then:

If $c$ and $d$ are the roots of $x^2+ax+b=0$,then a root of $x^2+(4c+a)x+(b+2ac+4c^2)=0$ is

Let $a$ be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation $x^3 - ax^2 + ax - 1 = 0$ is identical to the original cubic equation,then $a =$

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