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:

Let $\alpha, \beta$ be the roots of the quadratic equation $12x^{2}-20x+3\lambda=0$, where $\lambda \in \mathbb{Z}$. If $\frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}$, then the sum of all possible values of $\lambda$ is:

The roots of the equation $x^2 - 2\sqrt{2}x + 1 = 0$ are:

The solutions of the quadratic equation $(3|x| - 3)^2 = |x| + 7$ which belong to the domain of definition of the function $y = \sqrt{x(x - 3)}$ are given by

What is the product of the roots of the equation $(x - 2)^2 - 3(x - 2) + 2 = 0$?

If the roots of $4x^2 + px + 9 = 0$ are equal,then the absolute value of $p$ is: