The equation $x^2-4x+[x]+3=x[x]$,where $[x]$ denotes the greatest integer function,has:

If roots of the equation $ax^2 + bx + c = 0$ are $(\alpha - \beta)$ and $(\gamma - \delta)$,and roots of the equation $Ax^2 + Bx + C = 0$ are $(\alpha + \delta)$ and $(\beta + \gamma)$,then $\left| \frac{a}{A} \right|$ is equal to (where $D_1$ and $D_2$ are discriminants of the given equations respectively).

The least integer $k$ which makes the roots of the equation $x^2 + 5x + k = 0$ imaginary is

If $\alpha, \beta, \gamma$ are roots of $x^3 + x^2 - 5x - 1 = 0$,then the value of $[\alpha] + [\beta] + [\gamma]$ is (where $[.]$ denotes the greatest integer function):

If $1 - i$ is a root of the equation ${x^2} - ax + b = 0$,then $b = $

The sum of the real roots of the equation $x^4-2x^3+x-380=0$ is