If $\frac{1 + \sqrt{3}i}{2}$ is a root of the equation $x^4 - x^3 + x - 1 = 0$,then its real roots are:

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta=\gamma\delta=1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$,then $\frac{\alpha+\beta}{\gamma+\delta}=$

The roots of $ax^2 + b = 0$ are real and distinct if:

One of the real roots of the equation $x^3-6x^2+6x-2=0$ is

If the roots of the equation $x^2 - 8x + (a^2 - 6a) = 0$ are real,then:

If $x^{2/3} - 7x^{1/3} + 10 = 0,$ then $x = \dots$