Question

\[x^2 + 2x + 5 = 0\]

Answer 1

We have:

\[x^2 + 2x + 2 = 0\]

\[ \Rightarrow x^2 + 2x + 1 + 1 = 0\]

\[ \Rightarrow x^2 + 2 \times x \times 1 + 1^2 - (i )^2 = 0\]

\[ \Rightarrow (x + 1 )^2 - (i )^2 = 0\]

\[ \Rightarrow (x + 1 + i) (x + 1 - i) = 0\]

\[\Rightarrow (x + 1 + i) = 0\] or \[(x + 1 - i) = 0\]

\[\Rightarrow x = - 1 - i\] or \[x = - 1 + i\]

 Hence, the roots of the equation are 

\[- 1 + i \text { and }- 1 - i\].