Question

The number of complex roots of the equation:

$x^3+1+3x+3x^2=0$.

• A. $1$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is B $2$

$x^3+1+3x+3x^2=0$

$\Rightarrow (x+1{)}^3=0$

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

$\Rightarrow (x+1)=0or(x^2+x+1)=0$

$\Rightarrow x=-1$

But $\Rightarrow (x^2+x+1)=0$ have two complex roots as $\omega$ and ${\omega }^2$.

The number of complex roots of the equation $x^3+1+3x+3x^2=0$ is $2$.