$\{ x \in R:|x - 2|\,\, = {x^2}\} = $
$\{ -1, 2\}$
$\{1, 2\}$
$\{ -1, -2\}$
$\{1, -2\}$
The equation $x^2-4 x+[x]+3=x[x]$, where $[x]$ denotes the greatest integer function, has:
Let $y = \sqrt {\frac{{(x + 1)(x - 3)}}{{(x - 2)}}} $, then all real values of $x$ for which $y$ takes real values, are
The number of real solutions of the equation $\mathrm{x}|\mathrm{x}+5|+2|\mathrm{x}+7|-2=0$ is .....................
If $a,b,c$ are distinct real numbers and $a^3 + b^3 + c^3 = 3abc$ , then the equation $ax^2 + bx + c = 0$ has two roots, out of which one root is
Let $\alpha$ and $\beta$ be the two disinct roots of the equation $x^3 + 3x^2 -1 = 0.$ The equation which has $(\alpha \beta )$ as its root is equal to