Question

The roots of the equation $x^4-1=0$, are?

• A. $1,1,i,-i$
• B. $1,-1,i,-i$
• C. $1,-1,\omega ,{\omega }^2$
• D. None of these

Answer 1

Answer: (B)

$1,-1,i,-i$

$x^4-1=0$

$\Rightarrow$ $(x^2{)}^2-(1^2{)}^2=0$

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

$\Rightarrow$ Now, $x^2+1=0$ and $x^2-1=0$

$\Rightarrow$ $x^2=-1$ and $x^2=1$

$\Rightarrow$ $x=\pm \sqrt{-1}$ and $x=\pm 1$

$\Rightarrow$ $x=\pm i$ and $x=\pm 1$

$\therefore$ The roots are $1,-1,i,-i$