$4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}} = $

The sum of all real roots of the equation $|x-2|^2+|x-2|-2=0$ is:

The roots of the cubic equation $3x^3+4x^2-5x-2=0$ are diminished by $h$,and a cubic equation with these diminished roots is formed. If the transformed equation does not contain the $x^2$ term,then the roots of the transformed equation are

Let $z$ be a complex number such that the imaginary part of $z$ is non-zero and $a = z^2 + z + 1$ is real. Then $a$ cannot take the value

For what set of values of $p$ do the roots of the equation $3x^2 + 2x + p(p - 1) = 0$ have opposite signs?

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60^\circ$ is $\sqrt{7}Q$,then $P/Q$ is