Question

If $x\in [0,10]$, then the number of integral value(s) of $x$ satisfying the equation $x^2+4x+\left[x\right]+6=0$ (where [.] denotes the greatest integer function) is

Answer 1

From the given interval of $x$
$\left[x\right]\ge 0;x^2\ge 0;4x\ge 0\Rightarrow x^2+4x+\left[x\right]\ge 0\Rightarrow x^2+4x+\left[x\right]+6\ge 6$
Hence no solution exists