Question

Solve the following quadratic equation by factorization method only $x^2+1=0$

Answer 1

We have,
$x^2+1=0$

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

$\Rightarrow x^2-i^2=0[\because i^2=-1]$

$\Rightarrow (x+i)(x-i)=0[\because a^2-b^2=(a-b\left)\right(a+b\left)\right]$

$\Rightarrow x=iorx=-i$
Hence, the roots are $i$ and $-i$.