Question

The set $\{x:x^4=1$ and $x\in R\}$ is ...X... set. Here, $X$ refers to

• A. empty
• B. finite
• C. infinite
• D. singleton

Answer 1

Answer: (B)

Given equation is $x^4=1$
$\Rightarrow x^4-1=0$
$\Rightarrow \left(x^2-1\right)\left(x^2+1\right)=0$
$\Rightarrow (x-1)(x+1)=0$$\left(\because x^2\ne -1,x\in R\right)$
$\Rightarrow x=-1,1$
Hence, the given set is $\{-1,1\}$.