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Question
Solving the following quadratic equation by factorization method:
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
Solution
\[x^2 + \left( 1 - 2i \right) x - 2i = 0\]
\[ \Rightarrow x^2 + x - 2ix - 2i = 0\]
\[ \Rightarrow x\left( x + 1 \right) - 2i\left( x + 1 \right) = 0\]
\[ \Rightarrow \left( x + 1 \right)\left( x - 2i \right) = 0\]
\[ \Rightarrow \left( x + 1 \right) = 0 or \left( x - 2i \right) = 0\]
\[ \Rightarrow x = - 1, 2i\]
\[\text { So, the roots of the given quadratic equation are - 1 and 2i } . \]
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