${x \in R : |x - 2| = x^2} = $

The value of $k$ for which the equation $(k - 2)x^2 + 8x + (k + 4) = 0$ has both roots real,distinct,and negative is

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is

Let $p, q$ and $r$ be real numbers $(p \ne q, r \ne 0),$ such that the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign. Then the sum of squares of these roots is equal to:

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity, then $b + c$ is equal to

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 2x - 5 = 0$ and the equation $x^3 + bx^2 + cx + d = 0$ has roots $2\alpha + 1, 2\beta + 1, 2\gamma + 1$,then the value of $|b + c + d|$ is (where $b, c, d$ are constants):