Number of real roots of the equation [2 x3]-[7 x2]+[8 x]=x+2 is/are [ Note: [ k ] denotes greatest integer function less than or equal to k ]

Question

Number of real roots of the equation [2 x3]-[7 x2]+[8 x]=x+2 is/are [ Note: [ k ] denotes greatest integer function less than or equal to k ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

[2 x3]-[7 x2]+[8 x]=x+2 ⇒ x is an integer 2 x3-7 x2+8 x=x+2 ⇒ 2 x3-7 x2+7 x-2=0 ⇒ (x-1)(x-2)(2 x-1)=0 ⇒ x=1 text or 2

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

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

Q. Number of real roots of the equation [2x3]−[7x2]+[8x]=x+2 is/are [ Note : [k] denotes greatest integer function less than or equal to k ]

[2x3]−[7x2]+[8x]=x+2 ⇒x is an integer 2x3−7x2+8x=x+2 ⇒2x3−7x2+7x−2=0 ⇒(x−1)(x−2)(2x−1)=0 ⇒x=1 or 2

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

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