Question

The roots of the equation $x^3-3x-2=0$ are

• A. $-1,-1,2$
• B. $-1,1-2$
• C. $-1,2,3$
• D. $-1,-1,-2$

Answer 1

The correct option is B $-1,1-2$

$x^3-3x-2=0$

Clearly $x=-1$ is a solution of the equation, hence $(x+1)$ is a factor of the equation

$x^2-x-2$

_______________

$x+1)x^3-3x-2$

$x^3$ $+x^2$

__________________

$-3x-2-x^2$

$-x$ $-x^2$

___________________

$-2x-2$

$-2x-2$

____________

$0$

____________

Now roots of the equation $x^2-x-2=0$ will be roots of the given equation as well so,

$\Rightarrow x^2-x-2=0$

$\Rightarrow x^2+2x-x-2=0$

$\Rightarrow x(x+2)-1(x+2)=0$

$\Rightarrow (x-1)(x+2)=0$

Hence,

Factors $\Rightarrow (x+1)(x-1)(x+2)=0$

Roots $\Rightarrow -1,1,-2$.