If the roots of the equation $(m - n)x^2 + (n - l)x + (l - m) = 0$ are equal,then which of the following is true for $l, m,$ and $n$?

Let $\alpha \neq 1$ be a real root of the equation $x^3-a x^2+a x-1=0$,where $a \neq -1$ is a real number. Then,a root of this equation,among the following,is

If the roots of the equation $ax^2 + x + b = 0$ are real,then the roots of the equation $x^2 - 4\sqrt{ab}x + 1 = 0$ will be

If the roots of the equation $x^2 + 2x + p = 0$ are real,then what is the value of $p$?

Let the roots of the equation $E_1 \equiv x^3+x^2+lx+n=0$ be $x_i, (i=1, 2, 3)$ and the roots of $E_2 \equiv x^3+ax^2+bx+c=0$ be $\frac{x_i-1}{2}$. If the equation $E_2=0$ is a reciprocal equation of class one,then the roots of these two equations excluding the common roots are

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x - 60} = 1$ is: