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Question
x2 + 2x + 5 = 0
Solution
Given:
\[x^2 + 2x + 5 = 0\]
\[x^2 + 2x + 5 = 0\]
\[ \Rightarrow x^2 + 2x + 1 + 4 = 0\]
\[ \Rightarrow (x + 1 )^2 - (2i )^2 = 0 [(a + b )^2 = a^2 + b^2 + 2ab]\]
\[ \Rightarrow (x + 1 + 2i) (x + 1 - 2i) = 0 [ a^2 - b^2 = (a + b) (a - b)]\]
\[\Rightarrow (x + 1 + 2i) = 0\] or \[(x + 1 - 2i) = 0\]
\[\Rightarrow x = - (1 + 2i)\] or, \[x = - 1 + 2i\]
Hence, the roots of the equation are \[- 1 + 2i \text { and } - 1 - 2i\]
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