Question

Number of real roots of the equation $\left[2 x^3\right]-\left[7 x^2\right]+[8 x]=x+2$ is/are
$[$ Note : $[ k ]$ denotes greatest integer function less than or equal to $k$ ]

Answer 1

$\left[2 x^3\right]-\left[7 x^2\right]+[8 x]=x+2$
$\Rightarrow x$ is an integer
$ 2 x^3-7 x^2+8 x=x+2$
$ \Rightarrow 2 x^3-7 x^2+7 x-2=0$
$\Rightarrow (x-1)(x-2)(2 x-1)=0 $
$\Rightarrow x=1 \text { or } 2$