If ${x_1}, {x_2}, {x_3}$ are distinct roots of the equation $ax^2 + bx + c = 0$,then:

The solution of the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{3x}{p + q + r} = 0$ is

The equation whose roots are reciprocal of the roots of the equation $3x^2 - 20x + 17 = 0$ is

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then the set of possible values of $a$ is

The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

If the roots of the equation $ax^2 + bx + c = 0$ are real and of the form $\frac{\alpha}{\alpha - 1}$ and $\frac{\alpha + 1}{\alpha}$,then the value of $(a + b + c)^2$ is